Chapter 4, Problem 9STP

To determine

To Choose: The correct option.

Answer to Problem 9STP

Option D. $32\text{N}$

Explanation of Solution

Given:

The velocity-time graph depicting the motion of the cart.

Formula used:

The acceleration of an object can be obtained by,

  $a=\frac{\Delta v}{\Delta t}=\frac{v_f-v_i}{t_f-t_i}$

Where, $\Delta v$ is change in velocity in time interval $\Delta t$ .

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:

Considering the graph, the acceleration of the car can be calculated as follows:

Take time interval between $0\text{to}\text{4}\text{.0}\text{s}$ .

  $\begin{array}{c}a=\frac{v_2-v_1}{t_2-t_1}\\ =\frac{8.0-0}{4-0}\\ =2{\text{m/s}}^{\text{2}}\end{array}$

Then, the force exerted on a 16kg cart will be:

  $\begin{array}{c}{F}_{net}=ma\\ =16\times 2\\ =32\text{N}\end{array}$

Conclusion:

Thus, the force acting on the given cart is 32N.