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 $\xrightarrow[+ve] {}$ $x$(East) $ t=2 s$
Using, $ v=u+at$ $\Rightarrow $ $v \hat{i}=0+\vec{a}\times2$ or $\vec{a}$ $=\frac{v}{2} \hat{i}\qquad$
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.