Chapter 4, Problem 34A

Calculate the acceleration of a ball that starts from rest and rolls down a ramp and gains a speed of 25 m/s in 5 seconds.

From a rest position: $\text{Instantaneous}\text{speed}=\text{acceleration}\times \text{time}$

To determine

Theacceleration of a ball starting from rest and gaining a given speed and time of travel.

Answer to Problem 34A

The acceleration of the ball is $5\text{}{\text{m/s}}^2$.

Explanation of Solution

Given:

A ball initially at rest gains a speed of 25 m/s in 5 s.

Formula used:

The instantaneous speed, v of an object can be expressed in terms of its acceleration, a and time of travel t as,

$v=at$

For a given speed and time, the acceleration can be calculated as,

$a=\frac{v}{t}$

Calculation:

Here, the instantaneous speed of the ball is 25 m/s and the time is 5 s. Thus, the acceleration experienced by the ball is given by,

$\begin{array}{c}a=\frac{25}{5}\\ =5{\text{ m/s}}^2\end{array}$

Conclusion:

The acceleration of the ball is $5{\text{ m/s}}^2$ .