Chapter 3.1, Problem 6PP

To determine

The average acceleration of the race car during a particular time interval.

Answer to Problem 6PP

The average acceleration is $-7.{\text{0 m/s}}^2$

Explanation of Solution

Given:

The velocity of the race car changes from 36 m/s to 15 m/s in the time interval 3.0 s.

Formula Used:

The rate of change of velocity of the race car over a time interval, gives the average acceleration. It can be calculated as,

  $\begin{array}{c}a=\frac{dv}{dt}\\ =\frac{v_2-v_1}{t_2-t_1}\end{array}$

In the above equation, the subscript 1 denotes the initial value and 2 denotes the final value.

Calculation:

The velocity varies from $v_1=36.0\text{ m/s}$ to $v_2=15.0\text{ m/s}$ in the time interval $dt=3.0\text{ s}$ . Therefore, the average acceleration can be calculated as,

  $\begin{array}{c}a=\frac{15-36}{3}\\ =-7{\text{ m/s}}^2\end{array}$

The negative value of acceleration agrees with the slowdown of the race car.

Conclusion:

The average acceleration for the given time interval is $-7.{\text{0 m/s}}^2$ .