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

Solution

Physics sir · 4 steps

Differentiate the velocity to get acceleration, then multiply by mass in kilograms.

1. Find acceleration. Acceleration is the time derivative of velocity. Differentiate each component separately: d/dt(2t) = 2 and d/dt(3t²) = 6t.

   a⃗ = dv⃗/dt = 2î + 6t ĵ

2. At one second. At t = 1 s, a⃗ = (2î + 6ĵ) m s⁻². The mass is 500 g = 0.5 kg.
3. Newton's second law. F⃗ = ma⃗ = 0.5 × (2î + 6ĵ) = (î + 3ĵ) N. The î part matches the given 1 N, which confirms the working.
4. So. Comparing with (î + xĵ) N gives x = 3, option (d).

The idea to keep. When velocity is given as a function of time, differentiate it to get acceleration, then multiply by mass in kg. Use a known component of the force as a quick check.

Answer from the NTA final answer key. Solution by PrepWiser.