Chapter 4, Problem 78A

To determine

The force acting on the car.

Answer to Problem 78A

  $8000\text{N}$

Explanation of Solution

Given:

Mass of the car, $m=2000\text{ kg}$

Initial velocity, $v_i=0$

Final velocity, $v_f=24\text{m/s}$

Time elapsed, $t=6.0\text{s}$

Formula used:

Final velocity with constant acceleration is given by,

  $v_f=v_i+a\Delta t$

Where, $v_f$ is the final velocity, $v_i$ is the initial velocity, a is the acceleration and t is the time.

From Newton’s Second law of motion:

  $F_{net}=ma$

Where, a is the acceleration, m is the mass and $F_{net}$ is the net force.

Calculation:

Using the given values of initial and final velocities and the time taken, the acceleration of the car will be:

  $\begin{array}{c}{v}_f=v_i+a\Delta t\\ 24=0+a\left(6\right)\\ a=4{\text{m/s}}^{\text{2}}\end{array}$

Then, using Newton’s second law, the force acting on the 2000kg car can be calculated as follows:

  $\begin{array}{c}{F}_{net}=m\times a\\ =2000\times 4\\ =8000\text{N}\end{array}$

Conclusion:

Thus, the force acting on the car is 8000N.