Introduction to Motion and Its Parameters

Confused between scalar and vector? What is the difference between

distance and displacement? How are speed and velocity different from

each other? This seemingly easy terms always confuse us. Before we

jump right into the technicalities of motion, here are some basic

parameters of motion that will help you understand the topic well! 

Motion

The change in the position of the object with respect to time is called

the motion of that object. The change in motion is based on the

reference point of an individual. Let’s take an example of the 2 cars

(A and B) moving at a constant speed that you observe from your

school window.

From your reference point, the cars are in motion because they are

constantly moving. Although, from the reference point of the car A,

car B is not in motion since it has the same speed as car A. But you on

the other hand, for car A, will be in motion because of the constant

change in your position from the reference point of car A

Parameters of Motion

Scalar Quantity

These quantities only have a magnitude(size) and no directions.

Examples of such quantities are speed, mass, distance, volume and

many others.

Vector Quantity

These quantities have both magnitude and direction. So change in any

one of the two will change the value of the vector quantities.

Examples of vector quantities are velocity, acceleration, force,

displacement and many more.

Distance

The length of the total path travelled by the body is the distance

travelled by the body. It is the scalar quantity. Mostly measured in

m(meters).

Displacement

The length of the shortest path travelled by the body from point A to B

is the displacement. It is the scalar quantity. Mostly measured in

m(meters).

Speed

The distance travelled by the body per unit time is the speed of the

body. It is a scalar quantity. Speed is given by the formula,

speed=distance/time, Measured in m/s.

Uniform speed

If a body travels equal distance at equal intervals of time, the body is

said to be moving at a uniform speed.

Non-Uniform speed

If the speed of the body keeps changing throughout the body is said to

be moving at a non-uniform speed. The average speed of the body=

total distance travelled/total time taken to travel the distance.

Velocity

The displacement of a body from point A to B per unit time is the

velocity. It is a vector quantity, which means it has both magnitude

and direction. Velocity is given by the formula,

Velocity=displacement/time, Measured in m/s.

Uniform velocity

If a body travels equal distance at equal intervals of time in a straight

line the body is said to be moving at a uniform velocity.

Non-Uniform Velocity

If a body travels unequal distance at equal intervals of time in a

straight line the body is said to be moving at a non-uniform velocity.

The average velocity = total displacement/total time taken.

Acceleration

If a body changes its velocity with time, it is said to be accelerated.

Acceleration is defined as the rate of change of velocity with respect

to time. Its unit is m/s2.

Solved Examples on Parameters of Motion

Question: Unit of acceleration is

A. m/s

B. ms

C. m/s2

D. none of these

Solution: Option C. Acceleration = dv/dt. Unit of ‘v’ is m/s and ‘t’ is

s. Therefore, the unit of acceleration is m/s2.

Graphical Representation of Motion

Graphical Representation makes it simpler for us to understand data.

When analyzing motion, graphs representing values of various

parameters of motion make it simpler to solve problems. Let us

understand the concept of motion and the other entities related to it

using the graphical method. 

Graphical Representation of Motion

Using a graph for a pictorial representation of two sets of data is called

a graphical representation of data. One entity is represented on the

x-axis of the graph while the other is represented on the y-axis. Out of

the two entities, one is a dependent set of variables while the other is

independent an independent set of variables.

We use line graphs to describe the motion of an object. This graph

shows the dependency of a physical quantity speed or distance on

another quantity, for example, time.

Browse more Topics under Motion

● Introduction to Motion and its Parameters

● Equations of Motion

● Uniform Circular Motion

Distance Time Graph

The distance-time graph determines the change in the position of the

object. The speed of the object as well can be determined using the

line graph. Here the time lies on the x-axis while the distance on the

y-axis. Remember, the line graph of uniform motion is always a

straight line.

Why? Because as the definition goes, uniform motion is when an

object covers the equal amount of distance at equal intervals of time.

Hence the straight line. While the graph of a non-uniform motion is a

curved graph.

Velocity and Time Graph

A velocity-time graph is also a straight line. Here the time is on the

x-axis while the velocity is on the y-axis. The product of time and

velocity gives the displacement of an object moving at a uniform

speed. The velocity of time and graph of a velocity that changes

uniformly is a straight line. We can use this graph to calculate the

acceleration of the object.

Acceleration=(Change in velocity)/time

For calculating acceleration draw a perpendicular on the x-axis from

the graph point as shown in the figure. Here the acceleration will be

equal to the slope of the velocity-time graph. Distance travelled will

be equal to the area of the triangle, Therefore,

Distance traveled= (Base × Height)/2

Just like in the distance-time graph, when the velocity is non-uniform

the velocity-time graph is a curved line.

Solved Examples for You

Question: The graph shows position as a function of time for an object

moving along a straight line. During which time(s) is the object at

rest?

I. 0.5 seconds

II. From 1 to 2 seconds

III. 2.5 seconds

A. I only

B. II only

C. III only

D. none

Solution: Option B. Slope of the curve under the position-time graph

gives the instantaneous velocity of the object. The slope of the curve is

zero only in the time interval 1 < t < 2 s. Thus the object is at rest (or

velocity is zero) only from 1 to 2 s. Hence option B is correct.

Equations of Motion

Cricket fan? Hockey fan? Soccer fan? What is the first thing that is

taught when you first start training for these or any other sports? It is

understanding the correct motion, speed acceleration or the Equations

of Motion. Once you master the Equations of Motion you will be able

to predict and understand every motion in the world.

Equations of Motion For Uniform Acceleration

As we have already discussed earlier, motion is the state of change in

position of an object over time. It is described in terms of

displacement, distance, velocity, acceleration, time and speed.

Jogging, driving a car, and even simply taking a walk are all everyday

examples of motion. The relations between these quantities are known

as the equations of motion.

In case of uniform acceleration, there are three equations of motion

which are also known as the laws of constant acceleration. Hence,

these equations are used to derive the components like

displacement(s), velocity (initial and final), time(t) and

acceleration(a). Therefore they can only be applied when acceleration

is constant and motion is a straight line. The three equations are,

● v = u + at ● v² = u² + 2as ● s = ut + ½at²

where, s = displacement; u = initial velocity; v = final velocity; a =

acceleration; t = time of motion. These equations are referred as

SUVAT equations where SUVAT stands for displacement (s), initial

velocity (u), final velocity (v), acceleration (a) and time (T)

Browse more Topics under Motion

● Introduction to Motion and its Parameters ● Graphical Representation of Motion ● Uniform Circular Motion

Derivation of the Equations of Motion

● v = u + at

Let us begin with the first equation, v=u+at. This equation only talks

about the acceleration, time, the initial and the final velocity. Let us

assume a body that has a mass “m” and initial velocity “u”. Let after

time “t” its final velocity becomes “v” due to uniform acceleration

“a”. Now we know that:

Acceleration = Change in velocity/Time Taken

Therefore, Acceleration = (Final Velocity-Initial Velocity) / Time

Taken

Hence, a = v-u /t or at = v-u

Therefore, we have: v = u + at

● v² = u² + 2as

We have, v = u + at. Hence, we can write t = (v-u)/a

Also, we know that, Distance = average velocity × Time

Therefore, for constant acceleration we can write: Average velocity =

(final velocity + initial velocty)/2 = (v+u)/2

Hence, Distance (s) = [(v+u)/2] × [(v-u)/a]

or s = (v² – u²)/2a

or 2as = v² – u²

or v² = u² + 2as

● s = ut + ½at²

Let the distance be “s”. We know that

Distance = Average velocity × Time. Also, Average velocity =

(u+v)/2

Therefore, Distance (s) = (u+v)/2 × t

Also, from v = u + at, we have:

s = (u+u+at)/2 × t = (2u+at)/2 × t

s = (2ut+at²)/2 = 2ut/2 + at²/2

or s = ut +½ at²

Learn more:

1. Newtons Law of Motion 2. Uniform Circular Motion

More Solved Examples For You

Example 1: A body starts from rest accelerate to a velocity of 20 m/s

in a time of 10 s. Determine the acceleration of the boy.

Solution: Here, Final velocity v = 20 m/s and initial velocity u = 0 m/s

(the body was at rest yo!). Therefore, Time taken t = 10 s. Hence,

using the equation v = u +at.

a = (v-u )/t

= (20 – 0 ) /10

= 2 m/s2

Hence the acceleration of the body is 2 m/s2.

Example 2: A bus starts from rest and moves with constant

acceleration 8ms−2. At. the same time, a car travelling with a constant

velocity 16 m/s overtakes and passes the bus. After how much time

and at what distance, the bus overtakes the car?

A) t =4s, s = 64m B) t = 5s, s = 72m C) t = 8s, s = 58m D)

None of These

Solution: A) Let the position of the bus be PB and the position of the

car be PC. From s = ut +½ at², we have

Since the initial velocity of the bus, u = 0, hence we have PB = ½ (8)t²

And PC = velocity × Time = 16×t. For the bus to overtake the car, we

must have: PB = PC

Hence, ½ (8)t² = 16×t. Therefore, t = 4s.

Using the value of t = 4s in PB = ½ (8)t ², we have the position of the

bus at the time of overtaking is = 64m.

Uniform Circular Motion

Your friend has been kidnapped by aliens and she is kept in a circular

moving object. You need to save her but don’t know how the thing

works. In order to save her, you must understand the mechanics of this

weird circular moving object so that you can defeat it. Let us help you

with the basics of uniform circular motion. 

Uniform Circular Motion

Uniform motion can be defined as the motion of a body following a

circular path at a constant speed. The body has a fixed central point

and remains equidistant from it at any given position. When an object

goes around in a circle, the description of its motion becomes

interesting in many ways.

To better understand the circular motion let us look at an example.

You have a ball attached to a string and you move it constantly in a

circular motion. Here we observe two things:

● The speed of the ball is constant. It traces a circle with a fixed

centre.

● At every point of its motion, the ball changes its direction.

Therefore, we can say that in order to stay on a circular path,

the ball has to change its direction continuously.

From the second point, an important result follows. Newton’s first law

of motion tells us that there can be no acceleration without a net force.

So there must be a force associated with the circular motion. In other

words, for the circular motion to take place a net force has to act on

the object. The change in direction is a result of a centripetal force.

Centripetal force is the force acting on a body in a circular path. It

points towards the centre around which the body is moving.

As long as the ball is attached to the string, it will continue to follow

the circular path. The moment the string breaks or you let go of the

string, the centripetal force stops acting and the ball flies away. To

study uniform circular motion, we define the following terms.

Browse more Topics under Motion

● Introduction to Motion and its Parameters

● Graphical Representation of Motion

● Equations of Motion

Learn more about Motion in Different Acceleration for Different Time

Intervals.

Terminologies of Uniform Circular Motion

Time Period (T)

Time period (T) is the time taken by the ball to complete one

revolution. It is denoted by ‘T’. If ‘r’ is the radius of the circle of

motion, then in time ‘T’ our ball covers a distance = 2πr. Let us

assume the ball takes 3 seconds to complete one revolution. So T= 3

secs.

Frequency (f)

The number of revolutions our ball completes in one second is the

frequency of revolution. We denote frequency by f and f = 1/T. The

unit of frequency is Hertz (Hz). One Hz means one revolution per

second. Here the frequency will be 1/3 Hz.

Centripetal Force

We saw earlier that a body moving in a circle changes its direction

continuously. Therefore, we said that circular motion is an accelerated

motion. From Newton’s laws, we know that a body can accelerate

only when acted upon by some force.

In case of circular motion, this force is the centripetal force. If ‘m’ is

the mass of the body, then the centripetal force on it is given by F =

mv2/r; where ‘r’ is the radius of the circular orbit.

Angular Speed

We can also get an idea of how fast an object is moving in a circle if

we know how fast the line joining the object to the centre of the circle

is rotating. We measure this by measuring the rate at which the angle

subtended at the centre changes. This quantity is ω and ω = Change in

angle per unit time. Hence, ω is the Angular Speed.

The SI unit is radian / s or rad/s. For a single rotation, the change in

angle is 2π and the time taken is ‘T’, therefore we can write:

ω = 2π/T = 2πν …(4)

It is usually measured in r.p.m or rotations per minute. ω = 1 r.p.m, if

a body completes one rotation per minute. Also we can convert r.p.m

to radians per second as i r.p.m. = 2π/60s = π/30 rad/s

Solved Examples For You

Q: A car runs at constant speed on a circular track of radius 100 m

taking 62.8 s on each lap. What are the average speed and average

velocity on each complete lap? (π=3.14)

A. velocity = 10 m/s and speed = 10 m/s

B. speed = 10 m/s and velocity = 0 m/s

C. velocity = 0 m/s and speed = 0 m/s

D. velocity = 10 m/s and speed = 0 m/s

Solution: B). A closer look would tell you that all the other options

must be wrong, without solving it. Since in circular motion, if the

particle returns to the starting position, the displacement = 0. hence,

for such motion the velocity = 0 while as speed is non-zero. Now, we

have circumference of each lap = 2(3.14)(100) = 628 m. Therefore,

speed after each lap = 628/62.8 = 10 m/s