Question

A toy of mass 20 g at rest acquires a velocity $ (3\hat{i} - 2\hat{j}) $ ms$ ^{-1} $ in 2 seconds. Then the power of the toy is

• A. 0.975 W
• B. 0.325 W
• C. 1.3 W
• D. 0.065 W

Hint:

Ensure consistent SI units. Power is the rate of work done.

Answer 1

The Correct Option is D

Step 1: Convert mass to kg.
$ m = 0.02 \, \text{kg} $
Step 2: Find initial and final velocities.
$ \hat{v}_i = 0 \, \text{ms}^{-1} $ $ \hat{v}_f = (3\hat{i} - 2\hat{j}) \, \text{ms}^{-1} $
Step 3: Calculate work done.
$ W = \Delta KE = \frac{1}{2} m |\vec{v}_f|^2 - \frac{1}{2} m |\hat{v}_i|^2 $ $ |\hat{v}_f|^2 = 3^2 + (-2)^2 = 13 $ $ W = \frac{1}{2} (0.02) (13) - 0 = 0.13 \, \text{J} $
Step 4: Calculate power.
$ P = \frac{W}{t} = \frac{0.13}{2} = 0.065 \, \text{W} $
Step 5: Conclusion.
Power is 0.065 W.