Chapter 8, Problem 61A

A 20.0-kg mass moving at a speed of 3.0 m/s is stopped by a constant force of 15.0 N. Show that the stopping time required is 4.0 s.

To determine

To Show: The required stopping time period is 4.0s.

Explanation of Solution

Given info:

Mass, $m=20.0\text{ kg}$

Initial speed, $u=3.0\text{m/s}$

Final speed, $v=0$

Constant force, $F=15\text{N}$

Formula used:

According to the definition of impulses, impulse is equal to the change in momentum, which is given by:

Impulse = change in momentum

And, the time is calculated as,

  $\begin{array}{l}F\times \Delta t=m\times \Delta v\\ \Delta t=\frac{m\times \Delta v}{F}\end{array}$

Calculation:

Substitute the values and solve:

  $\begin{array}{l}ti\Delta t=\frac{m\times \Delta v}{F}\\ =\frac{20.0\text{kg}\times 3\text{m/s}}{15.0\text{N}}\\ =4\mathrm{s}\end{array}$

Conclusion:

Thus, the stopping time period is 4.0 s.