Ncert Exercises & Solutions

Question 6.20:

A body of mass 0.5 kg travels in a straight line with velocity $v = {ax}^{3 / 2}$ where $a = 5 m^{- 1 / 2} s^{- 1}$ . What is the work done by the net force during its displacement from x = 0 to x = 2 m?

Mass of the body, m = 0.5 kg

Velocity of the body is governed by the equation, $v = {ax}^{3 / 2} with a = 5 m^{- 1 / 2} s^{- 1}$

Initial velocity, u (at x = 0) = 0

Final velocity v (at x = 2 m) = $10 \sqrt{2}$ m/s

Work done, W = Change in kinetic energy

$= \frac{1}{2} m (v^{2} - u^{2})$
$= \frac{1}{2} \times 0.5 [{(10 \sqrt{2})}^{2} - {(0)}^{2}]$
$= \frac{1}{2} \times 0.5 \times 10 \times 10 \times 2 = 50 J$

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