Ncert Exercises & Solutions

Q. 20 The velocity of a body of mass 2 kg as a function of t is given by $v (t) = 2 t \hat{i} + t^{2} \hat{j} .$ Find the momentum and the force acting on it, at time t = 2 s.

Hint: Acceleration =

\frac{dv (t)}{dt}

Step 1: Calculate velocity at time, t=2 sec

Given, mass of the body m = 2 kg.

The velocity of the body $v (t) = 2 t \hat{i} + t^{2} \hat{j}$

$∴$ The velocity of the at t = 2S

$v = 2 \times 2 \hat{i} + (2)^{2} \hat{j} = (4 \hat{i} + 4 \hat{j})$

Step 2: Calculate the momentum

The momentum of the body (p) = mv

$= 2 (4 \hat{i} + 4 \hat{j}) = (8 \hat{i} + 8 \hat{j}) kg - m / s$

Step 3: Calculate acceleration at time, t = 2 sec

Acceleration of the (a) = dv/dt

$\begin{array}{l} = \frac{d}{dt} (2 t \hat{i} + t^{2} \hat{j}) \\ = (2 \hat{i} + 2 t \hat{j}) \\ At t = 2 s \\ a = (2 \hat{i} + 2 \times 2 \hat{j}) \\ = (2 \hat{i} + 4 \hat{j}) \end{array}$

Step 4: Calculate force acting on the body

Force acting on the body (F) = ma

$\begin{array}{l} = 2 (2 \hat{i} + 4 \hat{j}) \\ = (4 \hat{i} + 8 \hat{j}) N . \end{array}$

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