Question

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

• A. $\frac{mv}{2}$ eastwards 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)

$\frac{mv}{2}$ eastward and is due to the friction on the tyres exerted by the road.

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