Question

The velocity of a body of mass 2 kg as a function of time t is given by $v(t)=2t\hat{i}+t^{2}\hat{j}.$ The force acting on it, at time $t=2$ s is given by ________.

• A. $(4\hat{i}+4\hat{j})$ N
• B. $(2\hat{i}+2\hat{j})$ N
• C. $(4\hat{i}+2\hat{j})$ N
• D. $(4\hat{i}+8\hat{j})$ N

Hint:

Acceleration is the first derivative of velocity with respect to time.

Answer 1

The Correct Option is D

Step 1: Concept
Force ($\vec{F}$) = $m \vec{a} = m(d\vec{v}/dt)$.
Step 2: Analysis
Mass ($m$) = 2 kg. $\vec{v}(t) = 2t\hat{i} + t^2\hat{j}$. $\vec{a}(t) = d\vec{v}/dt = 2\hat{i} + 2t\hat{j}$.
Step 3: Calculation
At $t = 2$ s, $\vec{a}(2) = 2\hat{i} + 2(2)\hat{j} = 2\hat{i} + 4\hat{j}$. $\vec{F} = 2 \times (2\hat{i} + 4\hat{j}) = 4\hat{i} + 8\hat{j}$ N.
Step 4: Conclusion
Hence, the force acting is $(4\hat{i} + 8\hat{j})$ N.
Final Answer:(D)