Question

A car of mass m starts form rest and acquires a velocity along east $\overrightarrow{v} = v\widehat{i}$ (v > 0 ) 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)

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

Answer 2

Here

Mass of the car = m

Initial velocity $u = 0$ (as the car starts from rest)

Final velocity $\overset{\rightarrow}{v} = v\overset{\land}{i}$along east

$\overset{\rightarrow}{\quad + ve\quad}x(East)$

T = 2s

Using $v = u + at$at

$v\overset{\land}{i} = 0 + \overset{\rightarrow}{a} \times 2or\overset{\rightarrow}{a} = \frac{v}{2}\overset{\land}{i}$

Force exerted on the car is

$\overset{\rightarrow}{F} = m\overset{\rightarrow}{a} = \frac{mv}{2}\overset{\land}{i} = \frac{mv}{2}$

Eastward

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