Question

Velocity of a particle is v = v₀ + gt + ft². If its position at t = 0 is x = 0, then its displacement in unit time i.e. t = 1 is:

(a) v₀ + 2g + 3f

(b) \(v_0 + \frac{g}{2} + \frac{f}{3}\)

(c) \(v_0 + g + f\)

(d) \(v_0 + \frac{g}{2} + f\)

Answer 1

Correct option is : (b) \(v_0 + \frac{g}{2} + \frac{f}{3}\)

Given: v = v₀ + gt + ft²

or \(\frac{dx}{dt}\) = v₀ + gt + ft²

or dx = (v₀ + gt + ft²) dt

On integrating both sides,

Thus, alternative (b) is correct.