Ncert Exercises & Solutions

A body with a mass of $5$ kg is acted upon by a force $\vec{F}=( -3\hat{i} +4\hat{j})$ N. If its initial velocity at $t=0$ is $\vec{v}= ( 6\hat{i} -12\hat{j} )$ m/s, the time at which it will just have a velocity along the Y-axis is:
1. never
2. $10$ s
3. $2$ s
4. $15$ s

(b)

Hint: The final velocity along the x-axis is equal to zero.

Step 1: Find the acceleration of the particle.

Given, mass = 5 kg

\begin{array}{l} Acting force = \vec{F} = (- 3 \hat{i} + 4 \hat{j}) N \\ Initial velocity at t = 0, \vec{u} = (6 \hat{i} - 12 \hat{j}) m / s \\ Acceleration, \vec{a} = \frac{\vec{F}}{m} = (- \frac{3 \hat{i}}{5} + \frac{4 \hat{j}}{5}) m / s^{2} \end{array}

$\begin{array}{l} Acting force = \vec{F} = (- 3 \hat{i} + 4 \hat{j}) N \\ Initial velocity at t = 0, \vec{u} = (6 \hat{i} - 12 \hat{j}) m / s \\ Acceleration, \vec{a} = \frac{\vec{F}}{m} = (- \frac{3 \hat{i}}{5} + \frac{4 \hat{j}}{5}) m / s^{2} \end{array}$

Step 2: Put the final velocity along the x-axis equal to zero.

As final velocity is along Y-axis only, its x-component must be zero.

From v = u + at. As v_x = 0,

\Rightarrow 0 = 6 \hat{i} - \frac{3 \hat{i}}{5} t

$\Rightarrow 0 = 6 \hat{i} - \frac{3 \hat{i}}{5} t$

\Rightarrow t = \frac{5 \times 6}{3} = 10 s

$\Rightarrow t = \frac{5 \times 6}{3} = 10 s$

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