Question

A car is moving with a speed of $9m{s}^{-1}$. If the mass of the car is $2000kg$, find the magnitude of unbalanced force required to bring it to rest in three seconds.

• A. $3kN$
• B. $4kN$
• C. $6kN$
• D. $9kN$

Answer 1

The correct option is C $6kN$

Given: Mass, $m=2000kg$, initial velocity $u=9m{s}^{-1}$, final velocity $v=0$ (because the car is coming to rest), and time $t=3s$.
Let the acceleration required to bring the car to rest be $a$ and magnitude of unbalanced force be $F$.

Using first equation of motion:
$v=u+at\Rightarrow a=\frac{v-u}{t}=\frac{0-9}{3}=-3m{s}^{-2}$
The negative sign implies that car is decelerating.

Using Newton’s second law of motion:
$F=ma=2000\times (-3)=-6000N=-6kN$
Therefore an unbalanced force of magnitude $6kN$ is required to bring the moving car to rest. The negative sign indicates that the force is acting in a direction opposite to motion of the car.