Chapter 8, Problem 56A

A car with a mass of 1000 kg moves at 20 m/s. What braking force is needed to bring the car to a halt in 10 s?

To determine

Braking force required to bring a car to halt.

Answer to Problem 56A

  $2000\text{N}$

Explanation of Solution

Given:

Mass of car, $m=1000\text{kg}$

Initial speed, $u=20{\text{m/s}}^{\text{2}}$

Final speed, $v=0$

Time, $t=10\text{s}$

Formula Used:

From the equation of motion,

  $v=u+at$

Where, $v$ is initial speed , $u$ is final speed, $a$ is acceleration and $t$ is time

And from Newton’s second law, the net force is

  $F=ma$

Where, $m$ is mass and $a$ is acceleration.

Calculation:

Substituting the values in the equation of motion,

  $\begin{array}{l}0=20+a\times 10\\ \Rightarrow a=-\frac{20}{10}=-2{\text{m/s}}^2\end{array}$

So, deceleration is $2{\text{m/s}}^2$

Now, the needed braking force is

  $\begin{array}{c}{F}_{\text{braking}}=1000\times 2\\ =2000\text{N}\end{array}$

Conclusion:

Therefore, the braking force needed to bring the car at rest is $F_{\text{braking}}=2000\text{N}$ .