An object of mass 1000 g experiences a time-dependent force F = (2t i + 3t^2 j) N. The power generated by the force at time t is:

Given: Mass m = 1000 g = 1 kg and force F = (2t i + 3t^2 j) N. Find: Power generated by the force at time t. Using Newton's second law, a = Fm = 2t i + 3t^2 j Since velocity is obtained by integrating acceleration with respect to time, v = a dt = (2t i + 3t^2 j) dt = t^2 i + t^3 j Power is the dot product of force and velocity, P = F v Substituting, P = (2t i + 3t^2 j) (t^2 i + t^3 j) P = 2t^3 + 3t^5 Therefore, the power is 2t^3 + 3t^5 W and the correct option is D. The solution marks option A, but the working clearly gives 2t^3 + 3t^5, which matches option D.

An object of mass 1000 g experiences a time-dependent force F = (… — Solution | JEE Physics

MCQEasyJEE 2025Power

An object of mass $1000 \, \text{g}$ experiences a time-dependent force $\vec{F} = (2t \, \hat{i} + 3t^2 \, \hat{j}) \, \text{N}$ . The power generated by the force at time $t$ is:

A
$(2t^2 + 3t^3) \, \text{W}$
B
$(2t^2 + 18t^3) \, \text{W}$
C
$(3t^3 + 5t^5) \, \text{W}$
D
$(2t^3 + 3t^5) \, \text{W}$

Answer

Correct answer:D

Step-by-step solution

Standard Method

Given: Mass $m = 1000 \, \text{g} = 1 \, \text{kg}$ and force $\vec{F} = (2t \, \hat{i} + 3t^2 \, \hat{j}) \, \text{N}$ .

Find: Power generated by the force at time $t$ .

Using Newton's second law,

\vec{a} = \frac{\vec{F}}{m} = 2t \, \hat{i} + 3t^2 \, \hat{j}

Since velocity is obtained by integrating acceleration with respect to time,

\vec{v} = \int \vec{a} \, dt = \int (2t \, \hat{i} + 3t^2 \, \hat{j}) \, dt = t^2 \, \hat{i} + t^3 \, \hat{j}

Power is the dot product of force and velocity,

P = \vec{F} \cdot \vec{v}

Substituting,

P = (2t \, \hat{i} + 3t^2 \, \hat{j}) \cdot (t^2 \, \hat{i} + t^3 \, \hat{j})

P = 2t^3 + 3t^5

Therefore, the power is $2t^3 + 3t^5 \, \text{W}$ and the correct option is D.

The solution marks option A, but the working clearly gives $2t^3 + 3t^5$ , which matches option D.

Common mistakes

Using the listed answer key directly without checking the working. Here the solution labels option A, but the derivation gives $2t^3 + 3t^5$ , so the final choice must follow the working, not the mislabeled key.
Forgetting to convert mass $1000 \, \text{g}$ to $1 \, \text{kg}$ . The force is given in SI units, so mass must also be in SI units before applying $\vec{F} = m\vec{a}$ .
Using power as the product of magnitudes instead of the dot product. Instantaneous power is $P = \vec{F} \cdot \vec{v}$ , so the corresponding vector components must be multiplied and added.

Practice more Power questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step — free to start.

Start free trial More on Power

Answer

Step-by-step solution

Common mistakes

Practice more Power questions

Related questions