kinematics of line.ar motion

www.ktn.kptm.edu.my

LECTURER : TENGKU SARAH BINTI TENGKU AMRAN

IntroductionThere are 2 types of motion:

1) Linear or straight line motion (1-D)

• With constant (uniform) velocity

• With constant (uniform) acceleration eg : free fall motion

2) Projectile motion (2-D)

• X-component (horizontal)

• Y-component (vertical)

Straight line motion

Distance, d

• Scalar quantity• Always positive

• SI unit : m• Definition: total length of

travel from the initial position to the final

position

Displacement, s

• Vector quantity• can be positive, negative @ zero

• SI unit : m• Definition: the shortest distance

from the initial position to the final position

Straight line motion

Speed, v

• Scalar quantity• SI unit : ms-1

• Definition: the rate ofchange of distance

Velocity, v

• Vector quantity• SI unit : ms-1

• Definition: the rate of changeof displacement

• its direction is in the same directionof the change in displacement

change of distancetime interval

speed

dv t

change of displacement,time intervalav

av

velocity v

sv t

Straight line motionInstantaneous velocity, v

• Is defined as the instantaneous rate of change of displacement

• An object is moving in uniform velocity if

tancons tdsdt

lim

0

sv itt

t

v dsdt

Straight line motionAcceleration, a

• Vector quantity

• SI unit : ms-2

Average acceleration, aav

Is defined as the rate of change of velocity

• Its direction is in the same direction of motion

change of velocitytime intervalav

av

a

a vt

Straight line motionInstantaneous acceleration, a

• Is defined as the instantaneous rate of change of velocity

• An object is moving in uniform acceleration if

2

2

lim

0

va itt

t

sa dv ddt dt

tancons tdvdt

exercisesEX 1 : A toy train moves slowly along a straight

track according to the displacement, s against time, t graph in figure 1 below.

a. Explain qualitatively the motion of the toy train

b. Sketch a velocity (cm s-1) against time (s) graph.

c. Determine the average velocity for the whole journey

d. Calculate the instantaneous velocity at t=12s.

exercises

0

2

4

6

8

10

12

0 2 4 6 8 10 12 14 16t (s)

s (cm)

Figure 1

exercisesEX 2 : A velocity-time (v-t) graph in figure 2 below

shows the motion of a lift.

a. Describe qualitatively the motion of the lift

b. Sketch a graph of acceleration (m s-1) against time (s)

c. Determine the total distance traveled by the lift and its displacement

d. Calculate the average acceleration between 20 s to 40 s.

-6

-4

-2

0

2

4

6

0 5 10 15 20 25 30 35 40 45 50 55

t (s)

v (ms -1)

exercises

Figure 2

Kinematics eq.

+ at2 2v 2

1 221 22

1( )2

v uu as

s ut at

s vt at

s u v t

Kinematics equation for a particle moving along the x-axis with uniform acceleration are :

exercisesEX 3 : A particle moves along horizontal line

according to the equation

Where s is displacement in meters and t is time in seconds.

At time, t = 2 s, determine

a. The displacement of the particle

b. Its velocity

c. Its acceleration

3 2s=3t - 4t + 2t

exercisesEX 4 : A plane on a runway takes 16.2 s over a

distance of 1200 m to takes off from rest. Assuming constant acceleration during take off, calculate

a. The speed on leaving the ground

b. The acceleration during take off

exercisesEX 5 : A bus traveling steadily at 30 ms-1 along a

straight road passes a stationary car which, 5 s later begins to move with a uniform acceleration of 2 ms-2 in the same direction as the bus. Determine

a. The time taken for the car to acquire the same velocity as the bus

b. The distance traveled by the car when it is the same level with the bus

Free Fall Motion1) The direction of motion are now along the vertical

y-axis

2) Vector quantity (displacement, initial velocity, final velocity) are positive in an upward motion & negative in a downward motion.

3) The free fall acceleration is always negative in an upward & a downward motion

4) t is always positive.

Free Fall Motion

+ at2 2v 2

1 221 22

1( )2

v uu as

s ut at

s vt at

s u v t

Linear motion Free fall motion

- gt2 2v 2

1 221 22

1( )2

y y

y y y

y y

y y

y y y

g

g

v u

u gs

s u t t

s v t t

s u v t

exercisesEX 6 : A book is dropped 150 m from the ground.

Determine

a. The time taken for the book reaches the ground

b. The velocity of the book when it reaches the ground

(Given g = 9.81 ms-2)

exercisesEX 7 : A ball is thrown from the top of building is

given an initial velocity of 10 ms-1 straight upward. The building is 30 m high and the ball just misses the edge of the roof on its way down, as shown in figure 3 below. Calculate

a. The maximum height of the stone from point A.

b. The time taken from point A to C.

c. The time taken from point A to D.

d. The velocity of the stone when it reaches point D.

(Given g = 9.81 ms-2)

exercises

Figure 3