The velocity of a particle is v = v₀ + gt + Ft². Its position is x = 0 at t = 0; then its displacement after time (t = 1) is :

Solution

Physics sir · 3 steps

Velocity is given as a function of time, so integrate it from 0 to 1 to get the displacement.

1. Displacement from velocity. Velocity is the rate of change of position, v = dx/dt. So the displacement is the area under the v versus t curve, which is the integral of v over time.

   x = ∫₀¹ (v₀ + gt + Ft²) dt = [v₀ t + (g t²)/2 + (F t³)/3]₀¹

2. Put in limits. At t = 1 the bracket gives v₀ + g/2 + F/3. At t = 0 it gives 0, which matches x = 0 at the start.
3. So. The displacement after t = 1 is v₀ + g/2 + F/3, which is option (b).

The idea to keep. When velocity changes with time, never use x = vt. Integrate v term by term: each tⁿ becomes tⁿ⁺¹/(n+1).

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