Question

At any instant the velocity of a particle of mass 500 g is \((2t\hat{i}+3t^2\hat{j}) ms^{-1}\). If the force acting on the particle at t=1s is \((\hat{i} + x\hat{j})N\). Then the value of x will be:

• A. 6
• B. 4
• C. 3
• D. 2

Hint:

Differentiate velocity to find acceleration, and use F = ma to calculate force

Answer 1

The Correct Option is C

Step 1: Calculate acceleration.

\(\vec{v} = \frac{d}{dt} = (2t\hat{i} + 3t^2\hat{j})\)

\(\vec{a} = \frac{d\vec{v}}{dt} = (2\hat{i} + 6t\hat{j})\)

At t = 1s:

\(\vec{a} = (2\hat{i} + 6\hat{j}) ms^{-2}\)

Step 2: Calculate force.- Given mass m = 500g = 0.5kg:

\(\vec{F} = m\vec{a} = 0.5 \cdot (2\hat{i} + 6\hat{j}) = (\hat{i} + 3\hat{j})N\)

Final Answer: The value of x is 3