Question

A child is playing with a ball at the base of a hill. She rolls the ball up the hill with a speed of 8 m/s. After 23s, the ball comes back to her and has the same speed as when she rolled it but it's moving in the opposite direction. Assume that the ball's acceleration was constant as it rolled up and down the hill, and take the positive direction to point up the hill.

What was the ball's acceleration while rolling up and down the hill?

Answer 1

We have the equation of motion,

                                                                                     .......................................(1)

where v is final velocity, u is initial velocity, a is acceleration, s is displacement and t is time of motion.

In upward direction:

                     u = 8 m/s , v = 0 m//s , t = t₁ (say)

Therefore, we can write

                           

                       or,                                              ..............................(2)

In downward direction:

                     u = 0 m/s, v = -8 m/s, a =a and t = t₂ (say)

So, we can write

                    

                  or,                                                    ......................................(3)

From equation (2) and (3), it is clear that

                      

Since,

          

Therefore,

                          

Negative sign is showing that, the acceleration is in downward direction.

For any doubt please comment.