Chapter SH, Problem 2.10APP

To determine

To Calculate: The acceleration of the car.

Answer to Problem 2.10APP

The acceleration of the car is $\text{3}{\text{.0 m/s}}^2$ north.

Explanation of Solution

Given data:

The initial velocity of the car $=0\text{ km/h}$ (at rest)

The final velocity of the car $=108\text{ km/h north}$

The time taken by the car to accelerate $=10\text{ s}$

Formula used:

  $\text{acceleration}=\frac{\text{change in velocity}}{\text{time}}$

Calculation:

As per the problem,

The initial velocity of the car $=0\text{ km/h}$

The final velocity of the car $=108\text{ km/h north}$

Convert the velocity of the car in km/h to m/s using the ratios $\frac{1000\text{ m}}{1\text{ km}}=1$ and $\frac{\text{1 h}}{3600\text{ s}}=1$

Initial velocity, $v_i=0\frac{\text{km}}{\text{h}}\times \frac{1000\text{ m}}{1\text{ km}}\times \frac{1\text{ h}}{3600\text{ s}}=0\text{ km/h}$

Final velocity, $v_f=108\frac{\text{km}}{\text{h}}\times \frac{1000\text{ m}}{1\text{ km}}\times \frac{1\text{ h}}{3600\text{ s}}=30\text{ km/h}$

Change in velocity = final velocity − initial velocity

  $v_f-v_i=30\text{ m/s}-0\text{ m/s}=30\text{ m/s}$ north.

Time $=10\text{ s}$

Putting the values of change in velocity and time in the acceleration-formula

  $\begin{array}{l}\text{acceleration}=\frac{\text{change in velocity}}{\text{time}}\\ \text{acceleration}=\frac{30\text{ m/s}}{\text{10 s}}=3{\text{ m/s}}^2\end{array}$

Conclusion:

The acceleration of the car is $\text{3}{\text{.0 m/s}}^2$ north.