Ncert Exercises & Solutions

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

1.	$mv/2$ eastward and is exerted by the car engine.
2.	$mv/2$ eastward and is due to the friction on the tires exerted by the road.
3.	more than $mv/2$ eastward exerted due to the engine and overcomes the friction of the road.
4.	$mv/2$ exerted by the engine.

(b) Hint: The force is given by the rate of change of momentum.

Given, the mass of the car = m
As the car starts from rest, u = 0
Velocity acquired along with east = v

\hat{i}

$\hat{i}$
Duration = t = 2s.

Step 1: Find the acceleration of the particle.

We know that

\begin{array}{l} v = u + at \\ \Rightarrow v \hat{i} = 0 + a \times 2 \\ \Rightarrow a = \frac{v}{2} \hat{i} \\ Force, F = ma = \frac{mv}{2} \hat{i} \end{array}

$\begin{array}{l} v = u + at \\ \Rightarrow v \hat{i} = 0 + a \times 2 \\ \Rightarrow a = \frac{v}{2} \hat{i} \\ Force, F = ma = \frac{mv}{2} \hat{i} \end{array}$

Hence, the force acting on the car is mv/2 towards the east. As the external force on the system is only friction hence. the force mv/2 is by friction. Hence, force by the engine is an internal force.

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