Refer to the pair of tracks in Exercise 1. (a) On which track is the average speed greater? (b) Why is the speed of the ball at the end of the tracks the same? Exercise 1 Two balls are released simultaneously from rest at the left end of equal-length tracks A and B as shown. Which ball reaches the end of its track first?
Solution 41E Introduction We have to first find, in which track the ball will take less time to reach the end. Solution Step 1, solution of the exercise 1 (a) The first track has two part, the slope part (EF) and the flat part (FG). At the slope part, the ball will have acceleration and the velocity of the ball will increase till it reaches to the bottom of the slope. After the slope part the ball will move with constant velocity till the end of the track. In the second track, we can see three part. At the slope HI, the ball will attend the same velocity as in the EF part of the first track. Then from I to J, the ball will move with constant velocity. Hence till the point J, the first track and second track will take same time. Now the slope JK will accelerate the ball and LM will decelerate the ball in the same rate as the slope is same, hence the average velocity of the ball will be same as the flat part (FG) part of the first track. Now, at the part MN the ball will travel with same velocity as FG. But at the part KL, the ball will travel at higher velocity than FG. Hence we have seen that, except the part KL, the average velocity of the ball in track 1 and in track 2 will be same. But at the part KL the ball travels faster. Hence the overall average velocity of the ball will be higher at track 2. Since the total length is same, in the second track, the ball will reach the end faster.