Question

displacement is directly proportional to square of time then prove that object moves with constant acceleration

Answer 1

X(t) = X0 + V0*t + 0.5*A0*t^2
If your position is purely “proportional to the square of time,” then (if I understand you correctly), X0 = 0 and V0 = 0 (your initial position and your initial velocity, at time = 0, are both zero). Otherwise, you’d have an offset, and you wouldn’t be exactly proportional to the square of time.

Hope it helps u.

Answer 2

velocity-position. The first two equations of motion each describe one kinematic variable as a function of time. ... Velocity is directly proportional to time whenacceleration is constant (v ∝ t). Displacement is proportional to time squaredwhen acceleration is constant (∆s ∝ t2).