Question

A vehicle moving at $36\, km/hr$ is to be stopped by applying brakes in the next $5\, m$. If the vehicle weighs $2000\, kg,$ determine the average force that must be applied on it

• A. $10^4 N$
• B. $ 2 \times 10^4 N$
• C. $ 3 \times 10^4 N$
• D. $5 \times 10^3 N$
• E. $10^3 N$

Answer 1

Answer: (B)

Given, initial velocity of vehicle $u=36\, km / h$
$=10\, m / s$
Stopping distance of vehicle $s=5\, m$ and
mass of vehicle $m=2000\, kg$
So, from equation of motion
$v^{2}-u^{2}=2 a s$
since, final velocity of vehicle $v=0$ and acceleration of vehicle $=-a$ (acceleration)
$\Rightarrow -u^{2} =-2 a s $
$\Rightarrow a =\frac{u^{2}}{2 s} $
$=\frac{10 \times 10}{2 \times 5}=10\, m / s ^{2}$
The average force for braking
$F=m a=2000 \times 10=2 \times 10^{4} N$