Question

A car is moving at a speed of $16m{s}^{-1}$. A force causes it to accelerate at a rate of $2m{s}^{-2}$ for four seconds. If the mass of the car is $2000kg$, find the change in momentum caused by the force.

• A. $12000kgm{s}^{-1}$
• B. $14000kgm{s}^{-1}$
• C. $16000kgm{s}^{-1}$
• D. $18000kgm{s}^{-1}$

Answer 1

The correct option is C $16000kgm{s}^{-1}$

Given:
mass $m=2000kg$
initial velocity $u=16m{s}^{-1}$
time $t=4s$
and acceleration $a=2m{s}^{-2}$
Let the final velocity of the car be $v$, then
initial momentum of the car = $mu$
final momentum of the car = $mv$

Using the first equation of motion:
$v=u+at=16+2\left(4\right)=24m{s}^{-1}$

Change in momentum = final momentum - initial momentum
$\Rightarrow mv-mu=m(v-u)$
$\Rightarrow 2000(24-16)=16000kgm{s}^{-1}$
Therefore the change in momentum is $16000kgm{s}^{-1}$.