Question

A body of mass 1kg begins to move under the action of a time dependent force \(\overset{⃗}{F} = (t\hat{i}+3t^2\hat{j}) \text{N}\) where \(\hat{i}\) and \(\hat{j}\) are the unit vectors along x and y axis. The power developed by the above force at time \(t = 2 \text{s}\) will be (in watt)

• A. \(100\)
• B. \(50\)
• C. \(25\)
• D. \(5\)

Hint:

Find velocity by integrating acceleration, then use P = F dot v.

Answer 1

The Correct Option is A

Step 1: Work-energy view
Power is the rate of change of kinetic energy: $P = \frac{d}{dt}\left(\frac12mv^2\right)$.

Step 2: Evaluate
$v^2 = \frac{t^4}{4} + t^6$, so $KE = \frac12\left(\frac{t^4}{4}+t^6\right)$ and $P = \frac12\left(t^3 + 6t^5\right)$. At $t=2$: $\frac12(8+192) = 100$ W. Option (A).

Final Answer:
100 W. \[ \boxed{\text{(A)}\ 100\ \text{W}} \]