A powerboat, starting from rest maintains a constant acceleration. After a certain time Δt, its displacement and velocity are Δr and Δv. At time 2Δt, what will be its displacement and velocity, assuming the acceleration remains constant?

(A) 2Δr and 2Δv

(B) 2Δr and 4Δv

(C) 4Δr and 2Δv

(D) 4Δr and 4Δv

The correct option is C) 4Δr and 2Δv

Explanation:

Initially from rest means, initial velocity and displacement is zero.

AT time t = Δt,

Displacement (s) = Δr

velocity (v) = Δv

Now At t = 2Δt

By using the equation of motion

v = u + at

s = ut + (1/2) at²

Here,

v ∝ t and s ∝ t²

Increasing times by two time velocity will increase twice and displacement by four times

Displacement = 4Δr

Velocity = 2Δv