The acceleration experienced by a moving boat, after its engine is cut off, is given by `(dv)/(dt) = -kv^3`, where k is a constant If `v_0` is the magnitude of the velocity at cut off, find the magnitude of the velocity at a time t after the cut off.

A particle is moving with a constant speed v in a circle. What is the magnitude of average velocity after half rotation?

A motor boat is moving in a straight line. Its velocity is V when the motor is shut off. If the retardation at any subsequent time is equal to the magnitude to its velocity at that time, find its velocity and the distance travelled in time t after the motor is shut off.

A particle is moving in a vertical line whose equation of motion is given by s = 32 + 46t+9t^2 where 's' is measured in meters and 't' is measured in seconds. Find the velocity and acceleration of the particle at t=3 sec.

The velocity of a particle moving along the positive direction of x-axis is v= Asqrt(x) , where A is a positive constant. At time t = 0 , the displacement of the particle is taken as x = 0 . (i) Express velocity and acceleration as functions of time , and (ii) find out the average velocity of the particle in the period when it travels through a distance s ?

The acceleration of a particle moving along a straight line is (6t^(2)-3t)cm//s^(2) , at time t seconds. If the velocity of the particel at time 2 seconds be 10cm/s, find its velocity at time t seconds.

The velocity v of a particle is related to time t as v = 4+2 (c_(1)+c_(2)t) , where c_(1) and c_(2) are constants . Find out the initial velocity and acceleration.