Question

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

• A. $\frac{mv}{2}$ eastward and is exerted by the car engine
• B. $\frac{mv}{2}$ eastward and is due to the friction on the tyres exerted by the road
• C. more than $\frac{mv}{2}$ eastward exerted due to the engine and overcomes the friction of the road
• D. $\frac{mv}{2}$ exerted by the engine

Answer 1

Answer: (B)

Here, Mass of the car = $m$
Initial velocity, $u=0$ (As the car starts from rest)
Final velocity $\vec{v}$ $=v\hat{i}$ along east $\underset{+ve}{\to }$ $x$(East) $t=2s$
Using, $v=u+at$ $\Rightarrow$ $v\hat{i}=0+\vec{a}\times 2$ or $\vec{a}$ $=\frac{v}{2}\hat{i}$
Force exerted on the car is
$\vec{F}=m\vec{a}$ $=\frac{mv}{2}\hat{i}$ $=\frac{mv}{2}$ eastward
This is due to the friction on the tyres exerted by the road.