Question

A motor car running at the rate of $7m{s}^{-1}$ can be stopped by its brakes in 10 m. Prove that the total resistance to the motion, when the brakes are on, is one fourth of the weight of the car.

Answer 1

Initial velocity, $u=7m/s$

Distance traveled, $s=10m$

Final velocity, $v=0m/s$

According to equation of motion we know that,

$v^2-u^2=2as$

To determine acceleration consider the force acting on the car when breaks were applied that is

$F=\mu mg$

which will cause deceleration of the car $\therefore a=-\mu g$ by comparing $F=\mu mg$ and $F=ma$

Substitute in equation of motion above,

$v^2-u^2=2as=-2\mu gs$

$u^2=2\mu gs$

$\mu =\frac{u^2}{2gs}=\frac{49}{2\times 9.8\times 10}=\frac{1}{4}$

Therefore, force acting on the car when breaks were applied that is

$F=\mu mg=\frac{1}{4}mg=\frac{1}{4}W$ (as weight, $W=mg$)