The velocity of a particle is v = v₀ + gt + ft². If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is

A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity 'v' that varies as $$v = \alpha \sqrt x $$. The displacement of the particle varies with time as

A car starting from rest accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate $${f \over 2}$$ to come to rest. If the total distance traversed is 15 S, then

The relation between time t and distance x is t = ax² + bx where a and b are constants. The acceleration is