At any instant the velocity of a particle of mass 500 g is (2t î + 3t² ĵ) m s⁻¹. If the force acting on the particle at t = 1 s is (î + xĵ) N, then the value of x is:
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Question

At any instant the velocity of a particle of mass 500 g is (2t î + 3t² ĵ) m s⁻¹. If the force acting on the particle at t = 1 s is (î + xĵ) N, then the value of x is:

G1 Physics · Accepted Answer

Given velocity: v = 2t î + 3t² ĵ Acceleration is a = dv/dt = 2 î + 6t ĵ At t = 1 s: a = 2 î + 6 ĵ Mass: m = 500 g = 0.5 kg Therefore force: F = ma = 0.5(2 î + 6 ĵ) = î + 3 ĵ Comparing with F = î + xĵ, we get x = 3. Hence option C follows.