Question

A car of mass $1\times {10}^3\text{kg}$ travelling at a velocity $5\text{m/s}$ comes to rest in $2\text{sec}$, when it strikes a wall. What is the force exerted by the wall on car?

• A. $2\times {10}^3\text{N}$
• B. $2.5\times {10}^3\text{N}$
• C. $5\times {10}^3\text{N}$
• D. $4\times {10}^3\text{N}$

Answer 1

The correct option is B $2.5\times {10}^3\text{N}$


Let the force exerted by the wall on car be $F$
Using, impulse- momentum theorem:
$\text{Impulse}=P_f-P_i$
$+(F\times t)=m{v}_f-m{v}_i...\left(i\right)$
where, m is the mass of car, $m={10}^3\text{kg}$
Final velocity of car, $v_f=0$
Initial velocity of car, $v_i=-5\text{m/s}$
Time interval for action of impulsive force ,$t=2\text{sec}$
From the Eq. $\left(i\right)$:
$\Rightarrow F\times 2={10}^3[0-(-5\left)\right]$
$\therefore F=\frac{5}{2}\times {10}^3=2.5\times {10}^3\text{N}$