Chapter 3.1, Problem 8PP

To determine

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

Answer to Problem 8PP

The average acceleration is $\text{3}{\text{.0 m/s}}^2$

Explanation of Solution

Given:

A car initially moves downhill with a velocity $-3.0\text{ m/s}$ and this is over the time range 0 to 2.5 s . Then the car moves uphill with a velocity 4.5 m/s after 2.5 s.

Formula Used:

The rate of change of velocity of the 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 $v_1=-3.0\text{ m/s}$ to $v_2=4.5\text{ m/s}$ in the time interval $dt=2.5\text{ s}$ . Therefore, the average acceleration can be calculated as,

  $\begin{array}{c}a=\frac{4.5-\left(-3\right)}{2.5}\\ =3{\text{ m/s}}^2\end{array}$

The positive value of acceleration agrees with the uphill motion of the car.

Conclusion:

The average acceleration of the car for the given time interval is $3{\text{ m/s}}^2$ .