An object's displacement, s metres, from a fixed point after t seconds is s=5t^3+t^2. Find expressions for the object's velocity and acceleration at time t seconds.

Differentiating gives the rate of change and velocity and acceleration are rates of change. Velocity is the rate of change of displacement compared to time and acceleration is the rate of change of velocity compared to time. Therefore, differentiating an expression for displacement in terms of time, gives velocity and differentiating an expression for velocity in terms of time, gives acceleration.Therefore, v=15t^2+2t and a=30t+2