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Velocity-definition, types, practice problems, FAQs

Let’s assume your friend lives 10 km away from your home. The road between your home and your friend’s home is straight. If someone asks you, will you be able to reach his house? The answer is no. Why so? You require information about the direction in which you need to travel. Such quantities which are meaningful only when the magnitude and direction both are given are called vector quantities. Velocity is one such quantity. Velocity is defined as the displacement per unit time. In this article, we will explore more about velocity and its types.

Table of contents 

What is velocity?

The change in position vector or the displacement of a body divided by the time taken is called velocity. In the following diagram, the position vector of the body changes from point A to B. Displacement is defined as the shortest possible distance between two points. 



Motion between two points A and B

Imagine yourself cycling in a circular path of radius r as shown in figure.

Distance between points A and B =r

Displacement between points A and B =2r

It is a vector quantity. Velocity carries a SI unit of ms-1.

Velocity of an object is said to be positive if the body moves in the positive direction, and negative if it moves in the negative direction. 

Velocity vs speed

Though both of them have the same units, yet they are totally different. Speed is scalar, whereas velocity is a vector.

Average velocity

The total displacement covered by a body divided by the total time taken is called average velocity(vavg). In the following displacement time (s-t) graph, the average velocity in the time interval ab is equal to the slope of the graph between a and b.

vavg=Total displacementTotal time=st


s indicates the displacement undergone in time t.

Instantaneous velocity

The velocity of an object(v) at a particular instant of time is called “instantaneous velocity  vinst ”. If ds indicates displacement in time dt, then 

vinst =dsdt; dsdt indicates the derivative of displacement with respect to time at a given point, P in our case.


The graphical meaning of dsdt at point P is the slope of the graph at point P i.e the slope of the tangent drawn on the s-t curve at point P. Direction of instantaneous velocity at an instant is the same as the direction of average velocity for a straight line motion if the body does not reverse its direction of motion. Direction of instantaneous velocity at an instant may be opposite to the direction of average velocity for a straight line motion if the body reverses its direction of motion. 

Uniform and non-uniform motion

A motion is said to be uniform if the body covers equal distance in equal intervals of time. For eg. if a body covers 2 m of distance each second, the body is said to be in uniform motion. Whereas a motion is said to be non-uniform if the body covers unequal distances in equal intervals of time. A body in non-uniform motion is said to have acceleration.

Relative velocity

Motion is never absolute; it is always “relative”. It can only be defined wrt an observer. So, relative velocity is defined as the velocity of one body with respect to another.

The relative velocity of A wrt B can be written as vAB = vA- vB

Video explanation

Practice problems

1) A car A moves along east with a velocity of 20 ms-1. Another car B moves west with a speed of 40 ms-1. The relative velocity of A wrt B has magnitude 

(a)20 ms-1 (b)10 ms-1 (c)60 ms-1 (d) 25 ms-1

Soln) c

Given vA=20i;vB=-40i

The relative velocity of A wrt B; vAB=vA-vB=20i-(-40i)=60i

Hence, the velocity is 60 ms-1 

2) A police van is moving on a highway with a speed of 30 kmhr-1 fires a bullet at a thief car which is moving away in the same direction with a speed of 190 kmhr-1. If the muzzle speed of the bullet is 150 ms-1, find the speed of the bullet with respect to the thief's car.

Ans) Muzzle velocity of the bullet vBP=vB-vP=150 185=540 kmhr-1

Velocity of thief’s car, vT=190 kmhr-1

Since bullet is fired from the police car, the velocity of bullet, vB=540+30=570 kmhr-1 

Velocity of the bullet with respect to the thief , vBT= vB- vT= 570-190=380 kmhr-1

3)A particle moves along the x-axis. At a time t, the displacement is given by x=40+12t-t3. It’s x coordinate when it comes to rest ?

(a)24 m (b)40 m (c)56 m (d)16 m

Ans) c

When it comes to rest, velocity=0

v=dxdt=ddt(40+12t-t3)=12-3t2=0t=2 s

∴x(at t=2)=40+12(2)-(23)=56 m

4) A car travels with a velocity vu from X to Y. It returns from Y to X with a velocity vd. What is the average velocity of the car during this entire trip?


Average velocity =displacementTime taken

Since the displacement for the entire trip is zero, average velocity is zero.


Q.What is velocity?

Ans)Velocity is defined as the change in displacement divided by the change in time. 

Q.Is velocity a scalar or vector quantity?

Ans)Velocity is a vector quantity. It has direction.

Q.What is the difference between velocity and speed?

Ans) Velocity is total displacement divided by the total time taken. Speed is the total distance divided by the total time taken. Speed is a scalar quantity whereas velocity is a vector quantity.

Q.Is average velocity greater than average speed?

Ans) Average speed =Total distance Time taken

Average velocity=Total displacement Time taken

Since distance is greater than or equal to the magnitude of displacement, average speed is greater than or equal to average velocity. 

Related Topics:

Relative Motion-Definition, Solved examples, FAQs

Non-uniform accelerated motion - Definition, graphs, Solved examples, FAQs

Derivation of equations by Graphical method - 3 equations, Solved examples, FAQs

Motion under gravity - sign convention, Solved examples, FAQs

Graphs- velocity-time, acceleration time, interconversion, Solved examples, FAQs

Graphs- position-time, velocity-time, interconversion, Solved examples, FAQs


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