A car of mass m starts from rest and acquires a velocity along east
$v=v\hat{i}(v>0)$ in two seconds. Assuming the car moves with uniform acceleration, the force exerted on the car is

The correct option is A $\frac{mv}{2}$ eastward and is due to the friction on the tyres exerted by the road.
Step 1: Find acceleration.

Given,

Mass of $car=m$

As car starts from rest, therefore, $u=0$

Final velocity along east,$\overrightarrow{v}=v\hat{i}(v>0)$

$t=2s$

From $1^{s}t$ equation of motion

$v=u+at$


$v\hat{i}=0+\overrightarrow{a}\times 2$

$\overrightarrow{a}=\frac{v}{2}\hat{i}\dots \dots \dots ..\left(i\right)$

Step 2: Find the exerted force on the car.

Formula used: $\overrightarrow{F}=m\overrightarrow{a}$

$=\frac{mv}{2}\hat{i}$ (eastward) $\therefore$ a from equation (i)

This is due to the friction on the tyres exerted by the road.

Final Answer: (b)