Table of contents

• What is speed?
• Instantaneous speed
• Relative speed
• Average speed
• Uniform and non-uniform motion
• Practice problems
• FAQs

What is speed?

Speed can be defined as the ratio of the distance traveled (d) to the time taken (t). A car moving with a greater speed would be able to reach its destination faster compared to another car that is moving at a slower speed. Mathematically,

Speed=dt

Speed is a scalar quantity. The unit of speed is ms-1.

Average speed

The ratio of total distance traveled by a body to the total time taken by it to cover that distance is called the average speed.(vavg)

Average speed, vavg=Total distance traveledtotal time taken

A moving body always possesses a positive speed; speed can never be negative.

The slope of the displacement time graph gives average speed. Consider the following graph. If “s” indicates displacement in time “t”,then between two points a and b,

Average speed, vavg=st

Instantaneous speed

The instantaneous speed of a particle can be defined as the speed of a particle at a particular moment of time .

instantaneous speed, vinst = dsdt

i.e first derivative of s wrt time gives instantaneous speed.

Consider the following s-t graph which depicts a non-uniform motion. The tangent drawn to the curve at point P gives the slope at point P, ie. the value of instantaneous speed at that point.

Relative speed

Let us take for example, three athletes A,B and C who are running a race on the same track, parallel to each other. Now athlete A runs the fastest ,B is faster than C, however slower than A.

Fig shows three athletes A, B and C moving at different speeds. B is faster than C but is slower than A

Relative speed gives an idea how one body travels slower or faster in comparison to another. In this case, A moves at a greater speed compared to C, as A moves as compared to B.

The relative speed of A wrt B (when they are moving in the same direction) can be written as

vAB=vA-vB

Note: When A and B run in opposite directions, relative speed of A wrt B is

vAB=vA+vB

Uniform and non-uniform motion

A motion is said to be uniform if the body covers equal distances 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.

Video explanation

Speed: 4:14- 40:46

Practice problems

1) A body travels in a circular path of radius 7 m starting from A to B as shown in figure. The time taken to travel the distance AB is 2 s. What is the average speed of the body?

1. 22 m/s (b) 44 m/s (c) 33 m/s (d) 11 m/s

Solution)d.

The distance traveled along AB

=r=227×7=22 m

Speed =Distance Time taken=222=11 m/s

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

Solution)

Average speed =distance traveled Time taken

Let t1 and t2 be the times taken by the car to go from X to Y and from Y to X .

Then; t1+t2=XYvu+XYvd=XYvd+vuvuvd

vav=2XYt1+t2=2XYXYvd+vuvuvdvav=2vuvdvu+vd

3)Person A runs eastwards with a speed of 2 m/s and person B runs westwards with a speed of 1 m/s. What is the relative speed of A wrt B ?

Ans) Since A and B run in opposite directions, relative speed= 2 m/s+1 m/s=3 m/s

4)A car travels a total distance of d. If it travels the first half of the distance with a speed of 8 m/s; with what speed should it travel the second half so that the average speed comes out to be 12 m/s?

(a) 10 m/s (b)12 m/s (c)5 m/s (d)24 m/s

Ans)d

Solution

Let the car travel distance d/2 taking time t1 and the next part taking time t2

We have time t1=d2(8)=d16 ;time t2=d2(v) ; v=?

Since,

average speed =total distancetotal time=dt1+t2=12dd16+d2v=12

112=116+12v112-116=12v

Solving, we get v=24 m/s

FAQs

Q. What is speed? How is it different from velocity?

A. Speed is defined as the ratio of distance to the time taken. Speed is a scalar quantity. Velocity is displacement covered by an object divided by the time taken; and is a vector quantity.

Q. What is the unit of speed?

A. speed = distance traveled time taken

Distance traveled is the length, so it’s unit is m, and unit of time is s. So, unit of speed is ms-1.

Q. Can average velocity be greater than average speed?

A. Average speed =Total distance traveledtotal time taken ,

Average velocity =Total displacementtotal time taken

Let’s say a body moves from A to B along the semicircle. Now we can clearly see that distance is greater than the magnitude of displacement. Distance = magnitude of displacement for a straight line motion. So, average velocity can never be greater than average speed.

Q. Does the speedometer show us average or instantaneous speed?

A. The speedometer shows the speed at a given time. So, the speedometer shows us instantaneous speed.