Question

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 sec?



Answer is 2m/s BUT HOW​

Answer 1

Explanation:

See this problem in two chunks, one before collision another after collision.

Two collide with the bigger ball, the smaller ball has to travel 20 m forward with constant velocity 5m/s. Let the time consumed be t.

We know that velocity is rate of change of displacement.

i.e v = s/t

5 = 20 /t

t = 4 sec.

At this moment the balls collide and time in between collision can be neglected.

In the question it is asked average velocity from 0 to 6 seconds.

Before collision 4 sec have been consumed. In remaining 2 sec body travels backward with velocity 4 m/s. Let it covers a distance of s.

4 = s/2

s = 8m.

Let me remind you once again, velocity is displacement covered per unit time.

The ball moves 20 m forward and  8 m backward.

Therefore net displacement is 20 - 8 = 12 m , which is covered by body in 6 sec.

We know that,

$Average velocity(v) =\frac{Total displacement}{Total time}$,

Therefore v = 12/6

v = 2 m/s.

Hence average velocity is 2 m/s