Question

A car moving at $40$ km/h is to be stopped by applying brakes in the next $4.0$m. If the car weighs $2000$ kg what average force must be applied on it?

Answer 1

$1km=1000m$

$1h=3600s$

$1\frac{km}{h}=\frac{1000}{3600}=\frac{5}{18}\frac{m}{s}$

$v=\frac{40\times 5}{18}=\frac{100}{9}$

This is approximately $11.1\frac{m}{s}$.

$v{f}^2=v{i}^2+2\times a\times d,vf=0,d=4$

$0={\left(\frac{100}{9}\right)}^2+2\times a\times 4$

$a=\frac{{(-\frac{100}{9})}^2}{8}$

This is approximately $-15.432m/s^2$

Average force = $mass\times acceleration=2000\times \frac{{(-\frac{100}{9})}^2}{8}$

This is approximate $-30,864N$.