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XI / PHYSICS MOTION ALONG STRAIGHT LINE 11/PA

1

MOTION ALONG STRAIGHT LINE

Kinematics

It is the branch of physics which deals with study of motion of objects without taking into account the factors,

which cause motion. [Factors such as force, nature of bodies, mass etc.]

Motion

An object is said to be in motion if it changes its position with time, with respect to certain fixed frame of

reference [ i.e. surroundings]

e.g. A man walking on a road, bird flying in air, train moving on rails, etc.

Rectilinear motion

The type of motion in which a particle or a body moves along a straight line.

For example a car moving along straight road is in rectilinear motion.

Concept of point mass object

Whenever a body covers very large distances as compared to its own size, then it can be treated as point mass

object.

For example a car traveling a distance of 100 km, can be considered as point mass object.

Hence an object can be considered as a point mass object if during motion in a given time, it covers distances much

greater than its own size.

Motion in one dimension

Position of a body is always represented with the help of three coordinates, namely x, y and z coordinates.

If a body moves in such a way that during motion one out of three coordinates specifying position of object

changes with time then it is said to be having one dimensional motion.

All kinds of motion along straight line are examples of one dimensional motion e.g. motion under gravity [free

fall], motion of a car moving along straight road, motion of a train along straight rails etc.

Path length or distance

The length of the actual path traversed by an object during motion in a given internal of time is called distance

traveled by that object.

Suppose an object goes from A to D along the path shown in fig, then the distance traveled by object is given by

AB+BC+CD.

Properties

(1) It is scalar, i.e. has no direction.

(2) It is always positive i.e. can never be negative.

(3) SI units Metre (m).

A B

C

D



2

Displacement

The displacement is the shortest distance in a specified direction between the initial and final positions of the body.

From fig. displacement traveled by object is the vector joining A to D i.e. DA

Properties

(1) Displacement is a vector quantity i.e. has both direction and magnitude.

(2) Displacement of an object in a given interval of time can be positive, negative or zero.

(3) Magnitude of displacement of an object between any two points gives the shortest distance between them.

(4) It has SI units of length i.e. m

(5) It follows sign convention.

SPEED

It is equal to rate of change of position of the object during motion along any direction.

Practically speed is given by distance traveled per unit time taken by body.

time

cedisspeed

tan

Properties:

(1) speed is a scalar quantity.

(2) Speed is always positive and can never be zero.

(3) Its SI unit is m/s or ms-1

.

Uniform speed

If a body covers equal distances in equal intervals of time then it is said to be having uniform speed.

Average speed

Whenever a body moves with variable speed then we need to consider its average speed.

Average speed of a body is defined as the ratio of total distance traveled by body to the total time taken during its

journey.

Thus timetotal

cedistotalspeedAv

_

tan_.

Instantaneous speed

Speed of a body at any particular instant of time is called its instantaneous speed.

It is given as the ratio of very small distance traveled to very small time taken.

dt

dsspeedIns .

ds = very small distance, dt = very small time interval.

VELOCITY

Velocity of an object is defined ad the rate of change of its displacement from a given reference.

It is displacement traveled by object per unit time taken.

time

ntdisplacemevelocity

Properties



3

(1) It is a vector quantity i.e. has both direction and magnitude.

(2) Velocity of object can be positive, negative or zero.

(3) It follows sign convention.

(4) Its SI unit m/s or ms-1

.

Uniform velocity

An object is said to be having uniform velocity if it covers equal displacements in equal intervals of time.

If an object is having uniform velocity then it is said to be having uniform motion.

Variable velocity

If the object covers unequal displacement in equal intervals of time or vice versa then it is said to be having

variable velocity.

Average velocity:

Whenever a body is moving with variable velocity then we need to consider its average velocity.

Average velocity is the ratio of total displacement traveled to total time taken by body.

timetotal

ntdisplacemetotalvelocityAv

_

_.

POSITION TIME GRAPH OR X-T GRAPH

The graphical relation between displacement from a given reference and time is called x-t graph or position time

graph.

(a) Position time graph for a body at rest.

If a body is at rest, its displacement is not changing with time. Thus if a body is at rest then its x-t graph is always a

straight line parallel to time axis as shown.

(b) Position time graph for a body in uniform motion.

If a body is in uniform motion, it covers equal displacement in equal intervals of time. So its x-t graph is a straight

line inclined to time axis as shown.

x

t

x0

O

A

t1

x1

B x2

t2

C



4

Consider any two points A and B with coordinates (x1, t1) and (x2, t2) respectively.

Let BAC . From right triangle ACB we have

AC

BCTan

But BC = x2 – x1 and AC = t2 – t1

12

12

tt

xxTan

But Tanθ represent slope of the line, thus.

12

12

tt

xxslope

or takentime

ntdisplacemeinchangeslope

_

__

so velocityslope

Hence slope of x-t graph represent velocity of object.

(c) Position time graph for a body in uniformly accelerated motion:

If a body is having uniformly accelerated motion or positive acceleration then its x-t graph will be increasing

parabolic as shown.

(d) Position time graph for a body in retardation:

If a body is having negative acceleration, it has its x-t graph as decreasing parabola as shown.

VELOCITY TIME GRAPH

Graphical relation between the velocity of object and time taken is called v-t graph.

(a) Velocity time graph for a body at rest.

If a body is at rest, its velocity will be zero. Velocity of object will always be zero at all time. Hence v-t graph is a

straight line coincident with time axis.

x

t

x

t



5

(b) Velocity time graph for a body in uniform motion.

If a body has uniform motion, it has constant velocity, which does not change with time. Thus velocity time graph

will be straight line parallel to time axis as shown.

Consider two points A and B on the graph, with coordinates (v0, t1) and (v0, t2) respectively.

Consider the area of rectangle ABCD, we have:

DCBCABCDarea )(

)()()( 120 ttvABCDarea

So area under graph represent product of velocity and time, which is equal to displacement traveled by object.

Thus area under v-t graph represent displacement traveled by object in a given time interval.

(c) Velocity time graph for a body in uniformly accelerated motion.

If a body has uniformly accelerated motion, its velocity increases by equal amount in equal intervals of time.

So v-t graph is a straight line inclined to time axis as shown.

Consider any two points A and B on the graph with coordinates (v1, t1) and (v2, t2) respectively.

Let BAC . From right triangle ACB we have

AC

BCTan

A

t1

v1

B v2

t2

C

O

v

t

v0

O

A B

C D

t2 t1

v

t



6

But BC = v2 – v1 and AC = t2 – t1

12

12

tt

vvTan

but Tanθ represent slope of the line.

12

12

tt

vvslope

onacceleratislope

Hence slope of v-t graph represent acceleration of object.

(d) v-t graph for a body in retardation.

v-t graph for a body in negative acceleration i.e. retardation is also a straight line but of negative slope as

shown.

RELATIVE VELOCITY:

When two objects A and B are moving with different velocities, one object B observes A to be moving with certain

velocity.

The velocity with which A moves as observed by B is called relative velocity of A with respect to B.

Relative velocity of A with respect to B is given by:

BAAB vvv

---------------------------------------------------(1)

Where vA is the absolute velocity of A [Or velocity of A relative to ground] and vB is the absolute velocity of B [Or

velocity of B relative to ground].

In equation (1) values of velocities of A and B are substituted according to sign conventions as follows:

Sign conventions:

(1) All the velocities along right are taken as positive.

(2) All the velocities along left are taken as negative.

(3) All velocities above are positive.

(4) All velocities below are negative.

v

t O



7

Case-1:

If A and B are moving along same direction as shown.

Here velocities vA and vB are taken as positive, as both are along right direction.

Thus from eqn (1)

)()( BAAB vvv

BAAB vvv

Similarly velocity of B with respect to A.

)()( ABBA vvv

ABBA vvv

Case-2:

If both A and B are moving in opposite direction, A toward right and B towards left as shown.

Here vA is taken as positive and vB is taken as negative

Thus from eqn (1)

)( BAAB vvv

BAAB vvv

Similarly relative velocity B w.r.t A

ABBA vvv

)( ABBA vvv

B

A

Positive Negative

Negative

Positive

B

A



8

Case-3:

If vA and vB inclined to each other at an angle θ as shown.

Here relative velocity of A w.r.t. B or B w.r.t. A is given by

cos222

BABAAB vvvvv

ACCELERATION

Acceleration of a body is defined as the time rate of change of velocity of object.

Mathematically it is given as change in velocity of object per unit time taken.

takentime

velocityinchangeonaccelerati

_

__

Note:

(1) Acceleration is a vector quantity, and is taken along the direction of velocity of object.

(2) Its SI unit is m/s2.

(3) Acceleration can be negative positive or zero.

(4) Negative acceleration is called retardation.

Uniform acceleration:

A body is said to be having uniform acceleration if its velocity changes by equal amounts in equal intervals of time.

The motion of body is said to be uniformly accelerated motion.

Variable acceleration

If the velocity of body increased by unequal amounts in equal intervals of time or vice versa, it said to be having

variable or non uniform acceleration.

Average acceleration

When the body is moving with non uniform acceleration, we consider its average acceleration.

Average acceleration of a body is the ratio of total change in velocity to total time taken.

takentime

changevelocitynetonacceleratiAv

_

__.

EQUATIONS OF MOTION

Uniformly accelerated motion can be described by writing its equations of motion which are as follows:

atuv

Av

Bv



9

2

2

1atutS

asuv 222

Where symbols have their usual meaning.

Derivation of Equation of motion from v-t graph

Consider an object moving with a uniform acceleration a along a straight line. Let u be its initial velocity. The

velocity time graph of this motion is a straight line inclined to time axis, as shown in fig. Consider any two points

A and B on this graph where A has its coordinates (0,u), and (t,v) respectively.

From graph we have

OA = u

OC = EB = v

OE = AD = t.

(1) v =u + at:

We know that slope of velocity time graph of uniformly accelerated motion represents the acceleration of the

object.

Acceleration = slope of the v-t graph

AD

DBTanslopea

t

uv

OE

EDEBa

[from graph]

uvat

atuv -----------------------------------------------(1)

(2) 2

2

1atutS :

t

v

u D

B

t O

A

E

C



10

We know that, area under the velocity time graph represents the displacement covered by object in a given

time.

Thus displacement in time t is the area of trapezium OABE

ADEBOAS )(2

1

From graph putting values

OA = u

EB =v

AD = t.

tvuS )(2

1

now using (1) we get.

tatuuS )(2

1

)2(2

1 2atuS

Hence 2

2

1atutS ------------------------------------------------(2)

(3) asuv 222 :

Displacement traveled by object in time interval t is

S area of trapezium OABE

ADEBOAS )(2

1

From graph putting values

OA = u

EB =v

AD = t.

tvuS )(2

1

now using (1) put a

uvt

We have

))((2

1

a

uvuvS

a

uvS

2

22



11

Hence 222 uvaS

aSuv 222

In this way equation of motion are derived for uniformly accelerated motion.

DISPLACEMENT TRAVELED IN NTH

SECOND OF MOTION

Displacement traveled by an object in a particular second of motion can be calculated as follows:

Suppose

u = initial velocity of object

a = acceleration of object

nS = displacement traveled by object in first n seconds

1nS = distance traveled by object in (n-1) seconds of motion.

Displacement traveled in first n seconds of motion

2

2

1anunSn -----------------------------------------(1)

Distance traveled in first (n-1) seconds of motion

2

1 )1(2

1)1( nanuSn --------------------------------------(2)

From fig, displacement traveled in nth

second of motion

1 nnn SSD

Putting values from (1) and (2) we get

22 )1(

2

1)1(

2

1nanuanunDn

anaanuunanunDn 2

1

2

1

2

1 22

aanuDn2

1

)12(2

na

uDn

DERIVATION OF EQUATIONS OF MOTION BY CALCULUS METHOD

Consider an object moving in a straight line with uniform acceleration a.

Let

1nS

nS

nD

O A

B



12

u = initial velocity of object at t =0

v = final velocity of object at time instant t

S = displacement traveled by object in time interval from 0 to t.

(1) atuv

Let at an instant t , v be the velocity of object and dv be the change in velocity in time interval dt

dt

dvanaccelratio

adtdv

Integrating both sides, we get.

tv

u

adtdv0

tv

u

dtadv0

,

[As a is constant.]

tv

u tau 0][

0 tauv

atuv -----(1)

(2) 2

2

1atutS

Consider an object moving along straight line with uniform acceleration a . Let at any instant t, ds be the

displacement of the object in time interval dt . Its instantaneous velocity v is given by:

dt

dsv

vdtds

dtatuds )(

[from (1)]

atdtudtds

Integrating both sides.

atdtudtds

ttS

000



13

tdtadtuds

ttS

000

t

ts tatus

0

2

002

2

0

2]0[]0[

22tatuS

2

2

1atutS

(3) asuv 222

Consider a particle moving along straight line with initial velocity u and uniform acceleration a .

dt

dva

ds

ds

dt

dva

ds

dv

dt

dsa

ds

dvva

[ dt

dsv ]

vdvads

Integrating both sides

vdvdsa

v

u

S

0

v

u

s vsa

2

2

0

22

22 uvas

2

22 uvas



14

asuv 222

ASSIGNMENT

1. Read each statement below carefully and state with reasons and examples, if it is true or false. A particle in

one dimensional motion.

(a) With zero speed at an instant may have non zero acceleration at that instant.

(b) With zero speed may have non zero velocity.

(c) With positive value of acceleration must be speeding up.

2. Following figure gives the speed time graph of the motion of a car. What is the ratio of the distance traveled

by the car during the last two seconds to the total distance traveled in seven seconds?

3. The acceleration a of a body, starting from rest varies with time t according to the relation. 43 ta . Find

the velocity of the body at time t =2s. [Ans: 14 ms-1

]

4. A train covers half of its journey with a speed of 20 ms-1

and the other half with a speed of 30 ms-1

. Find the

average speed of the train over whole journey. [Ans: 24 ms-1

]

5. The displacement y of a body varies with time t as: 2163

2 2 tty . How long does the body take to

come to rest? [Ans: 12s]

6. Figure shows the velocity time graph of a body moving in a straight line. How much distance does it travel

during the last 10 seconds?

7. The velocity time graph of a stone thrown vertically upward with an initial velocity of 30 ms

-1 is shown.

The velocity in the upward direction is taken as positive and that in the downward direction as negative. What

is the maximum height to which the stone rises?



15

8. A body goes from A to B with a velocity of 40 kmh

-1 and returns from B to A with a velocity of 60 kmh

-1.

What is the average velocity of the body during the whole journey? [Ans: 0]

9. A stone falls freely from rest from the top of a tower and the total distance covered by it in the last second

of its motion equals the distance covered by it in the first three seconds of its motion. Find the time for which

stone remains in air and the height of the tower. [Ans: 5s, 125 m]

10. A parachutist drops freely from an aeroplane for 10 s before the parachute opens out. Then he descends

with a net retardation of 2.5 ms-2

. If he bails out of the plane at a height of 2495 m and g = 10ms-2

, find his

velocity on reaching ground. [Ans: 5 ms-1

]

11. A car accelerates from ret at a constant rate A for some time after which it decelerates at a constant rate B to

come to rest. If the total time elapsed is t, find the total distance traveled by the car. [Ans: 2

2

1t

BA

AB

]

12. A freely falling body, falling from a tower of height h covers a distance h / 2 in the last second of its

motion. Find the height of the tower. [Ans: 58 m]

13. Ball A is rolled in a straight line with a speed of 5 ms-1

towards a bigger ball B lying 20 m away. After collision

with ball B, ball A retraces the path and reaches its starting point with a speed of 4 ms-1

. What is the average

velocity of ball A during the time interval 0 to 6 s? [Ans: 2 ms-1

]

14. the following cases whether the motion is one two or three dimensional motion:

(a) a kite flying on a windy day

(b) a speeding car on a long straight highway

(c) a carom coin rebounding from the side of the board

(d) A planet revolving around its star.

15. A particle is moving along a circular track of radius r. What is the distance traversed by the particle in half

revolution? What is displacement?

16. Two straight lines drawn on the same displacement time graph make angles 300 and 60

0 respectively. Which

line represents the greater velocity? What is the ratio of the two velocities? [Ans: 1:3]

17. A ship moves due east at 12 km/hr for one hour and then turns exactly towards south to move for an hour at 5

km/hr. Calculate its average velocity for the given motion. [Ans: 6.5km/hr; 22o37’south of east]

18. A car travels along a straight line with speed 40 km/hr from A to B and returns back from B to A wit speed 60

km/hr. find the average speed of the car and its average velocity. [Ans: 48km/hr; 0]

19. A car traveled the first third of a distance x art a speed of 10 km/hr, the second third at a speed of 20 km/hr, and

the last third at a speed of 60km/hr. Determine the average speed of the car over the entire distance x. [Ans:

18km/hr]



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20. Two parallel rail tracks run from north to south. On one track, train A is moving from south to north with a

speed of 20 m/s. On the other track, train B is moving from north to south with a speed of 30 m/s. Find the

relative velocity of (i) A with respect to B, (ii) the ground with respect to A, and (iii) B with respect to the

ground. [Ans: (i) 50 m/s (ii) -20 m/s (iii) -30 m/s]

21. A train is moving south wards with a speed of 108 km/h. A monkey is running on the roof of the train with a

speed of 5 m/s with respect to the train. Find the velocity of the monkey as observed by a person standing on

the ground if the monkey is running (i) southwards, and (ii) north wards. [Ans: (i) -35 m/s (ii) -25 m/s]

22. A police van moving on a highway with a speed of 36 km/h fires a bullet at a thief’s car speeding away in the

same direction with a speed of 108 km/h. If the muzzle speed of the bullet is 140 m/s, with what speed will the

bullet hit the thief’s car? [Ans: 120 m/s]

23. A 15 m long train is going towards north with a speed of 10 m/s. How much time will a parrot, flying at 5 m/s

towards south, will take to cross the train? [Ans: 10 s]

24. A man walks on a straight road from his home to market 2.5 km away with a speed of 5 km/hr. Finding the

market closed he instantly turns and walks back home with a speed of 7.5 km/hr. What is the

(a) magnitude of average velocity and

(b) Average speed of the man.

25. A train covers half of its journey at a speed of 10 m/s and the other half at a speed of 15 m/s. What is the

average speed of the train during the whole journey? [Ans: 12 m/s]

26. A boy runs from his home to school at a speed of 4 m/s on a straight road and walks back to his home at a

speed of 2 m/s. Find his (i) average speed, and (ii) average velocity. [Ans: (i) 2.67 m/s (ii) 0]

27. A body describes 10 m in third second and 12 m in 5th

second with uniform acceleration. Find the distance

traveled by (i) next 3 seconds and (ii) 8th

second of its motion. [Ans: (i) 42 m (ii) 15 m]

28. A motor cyclist covers half of the distance between two places at a speed of 30 km/h and the second half at the

speed of 60 km/h. Compute its position and velocity at t = 2s. [Ans: 40 km/h]

29. From the top of a multi storied building 40 m tall, a boy projects a stone vertically upwards with an initial

velocity of 10 m/s such that it eventually falls to the ground. (i) After how long will the stone strike the

ground? (ii) After how long will it pass through the point from where it was projected? (iii) What will be its

velocity when it strikes the ground? Take g = 10 m/s2. [Ans: (i) 4s (ii) 2s (iii)-30 m/s]

30. A ball of mass 100 g is projected vertically upwards from the ground with a velocity of 49 m/s. At the same

time another identical ball is dropped from a height of 98 m to fall freely along the same path as followed by

the first ball. After sometime, the two balls collide. Find where from ground the balls collide. [Ans: 78.4 m]

31. A body travels 200 cm in the first two seconds and 220 cm in the next four seconds. What will be the velocity

of the body at the end of the seventh second from the start? [Ans: 10 cm/s]

32. A ball is thrown vertically upwards with a velocity of 20 m/s from a platform which is moving upwards with a

velocity of 5 m/s. Taking g =10 m/s2, find (a) the time taken by the ball to reach the highest point, (b) the

maximum height attained by it, (c) the total time taken by the ball to return to the platform and (d) the velocity

with which the ball strikes the platform. [Ans: (a) 2.5 s, (b) 31.25 m, (c) 4 s, (d) 15 m/s]

33. A body, moving in a straight line, with an initial velocity u and a constant acceleration a, covers a distance of

40 m in the 4th

second and a distance 60 m in the 6th

second. Find the values of u and a respectively. [Ans:

5ms-1

, 10ms-2

]



17

34. A bullet is fired vertically upwards with an initial velocity of 50 ms-1

. If g = 10 ms-2

, what is the ratio of the

distances traveled by the bullet during the first and the last second of its upward motion? [Ans: 9:1]

35. The driver of a train A moving at a speed of 30 ms-1

sights another train B moving on the same track at a speed

of 10ms-1

in the same direction. He immediately applies brakes and achieves a uniform retardation of 2 ms-2

. To

avoid collision, what must be the minimum distance between the trains? [Ans: 100 m]

NCERT QUESTIONS

36. In which of the following examples of motion, can the body be considered approximately a point object: (a) a

railway carriage moving without jerks between two stations. (b) a monkey sitting on top of a man cycling

smoothly on a circular track. (c) a spinning cricket ball that turns sharply on hitting the ground. (d) a tumbling

beaker that has slipped off the edge of a table.

37. The position-time (x-t) graphs for two children A and B returning from their school O to their homes P and Q

respectively are shown in Fig. 3.19. Choose the correct entries in the brackets below ; (a) (A/B) lives closer to

the school than (B/A) (b) (A/B) starts from the school earlier than (B/A) (c) (A/B) walks faster than (B/A) (d) A

and B reach home at the (same/different) time (e) (A/B) overtakes (B/A) on the road (once/twice).

38. A woman starts from her home at 9.00 am, walks with a speed of 5 km h–1 on a straight road up to her office

2.5 km away, stays at the office up to 5.00 pm, and returns home by an auto with a speed of 25 km h–1. Choose

suitable scales and plot the x-t graph of her motion.

39. A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps

forward and 3 steps backward, and so on. Each step is 1 m long and requires 1 s. Plot the x-t graph of his

motion. Determine graphically and otherwise how long the drunkard takes to fall in a pit 13 m away from the

start.

40. A jet airplane travelling at the speed of 500 km h–1

ejects its products of combustion at the speed of 1500 km h–

1 relative to the jet plane. What is the speed of the latter with respect to an observer on the ground ?

41. A car moving along a straight highway with speed of 126 km h–1

is brought to a stop within a distance of 200

m. What is the retardation of the car (assumed uniform), and how long does it take for the car to stop ?

42. Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 km h–1

in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1 m s–2

. If

after 50 s, the guard of B just brushes past the driver of A, what was the original distance between them ?

43. On a two-lane road, car A is travelling with a speed of 36 km h–1

. Two cars B and C approach car A in opposite

directions with a speed of 54 km h–1

each. At a certain instant, when the distance AB is equal to AC, both being



18

1 km, B decides to overtake A before C does. What minimum acceleration of car B is required to avoid an

accident ?

44. Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T

minutes. A man cycling with a speed of 20 km h–1

in the direction A to B notices that a bus goes past him every

18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus

service and with what speed (assumed constant) do the buses ply on the road?

45. A player throws a ball upwards with an initial speed of 29.4 m s–1

. (a) What is the direction of acceleration

during the upward motion of the ball ? (b) What are the velocity and acceleration of the ball at the highest point

of its motion ? (c) Choose the x = 0 m and t = 0 s to be the location and time of the ball at its highest point,

vertically downward direction to be the positive direction of x-axis, and give the signs of position, velocity and

acceleration of the ball during its upward, and downward motion. (d) To what height does the ball rise and after

how long does the ball return to the player’s hands ? (Take g = 9.8 m s–2

and neglect air resistance).

46. Read each statement below carefully and state with reasons and examples, if it is true or false ; A particle in

one-dimensional motion (a) with zero speed at an instant may have non-zero acceleration at that instant (b) with

zero speed may have non-zero velocity, (c) with constant speed must have zero acceleration, (d) with positive

value of acceleration must be speeding up.

47. A ball is dropped from a height of 90 m on a floor. At each collision with the floor, the ball loses one tenth of

its speed. Plot the speed-time graph of its motion between t = 0 to 12 s.

48. Explain clearly, with examples, the distinction between : (a) magnitude of displacement (sometimes called

distance) over an interval of time, and the total length of path covered by a particle over the same interval; (b)

magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average

speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show

in both (a) and (b) that the second quantity is either greater than or equal to the first. When is the equality sign

true ? [For simplicity, consider one-dimensional motion only].

49. A man walks on a straight road from his home to a market 2.5 km away with a speed of 5 km h–1. Finding the

market closed, he instantly turns and walks back home with a speed of 7.5 km h–1. What is the (a) magnitude

of average velocity, and (b) average speed of the man over the interval of time (i) 0 to 30 min, (ii) 0 to 50 min,

(iii) 0 to 40 min ? [Note: You will appreciate from this exercise why it is better to define average speed as total

path length divided by time, and not as magnitude of average velocity. You would not like to tell the tired man

on his return home that his average speed was zero !]

50. Look at the graphs (a) to (d) (Fig. 3.20) carefully and state, with reasons, which of these cannot possibly

represent one-dimensional motion of a particle.



19

NCERT ANSWERS

36. (a), (b)

37. (a) A....B, (b) A....B, (c) B....A, (d) Same, (e) B....A....once.

39. 37 s

40. 1000 km/h

42. 3.06 m s–2 ; 11.4 s 3.7 1250 m (Hint: view the motion of B relative to A)

43. 1 m s–2 (Hint: view the motion of B and C relative to A)

44. T = 9 min, speed = 40 km/h. Hint: v T / ( v – 20 ) =18; v T / ( v + 20 ) = 6

45. (a) Vertically downwards; (b) zero velocity, acceleration of 9.8 m s-2 downwards; (c) x > 0 (upward and

downward motion); v < 0 (upward), v > 0 (downward), a > 0 throughout; (d) 44.1 m, 6 s.

46 .(a) True;, (b) False; (c) True (if the particle rebounds instantly with the same speed, it implies infinite

acceleration which is unphysical); (d) False (true only when the chosen positive direction is along the direction

of motion)

49. (a) 5 km h–1, 5 km h–1; (b) 0, 6 km h–1; (c) 15 8 km h–1, 45 8 km h–1 3.15 Because, for an arbitrarily

small interval of time, the magnitude of displacement is equal to the length of the path.

50. All the four graphs are impossible. (a) a particle cannot have two different positions at the same time; (b) a

particle cannot have velocity in opposite directions at the same time; (c) speed is always non-negative; (d) total

path length of a particle can never decrease with time. (Note, the arrows on the graphs are meaningless).

xi / physics motion along straight line 11/pa - tejas engineers

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