A car is travelling with a velocity of "0.5t^2+t+2" m/s at t=0 (where t is in seconds), find the acceleration of the car at a) t=0 b)t=2

Acceleration can be described as the 'rate of change of velocity' as it is simply how quickly the car is increasing/decreasing in velocity. Therefore as the velocity is described as an expression of t - time in seconds after a certain point - and you know differentiation finds the gradient function of a polynomial, and as gradient is the rate of change of the polynomial, you can simply differentiate the expression for velocity with respect to t to find the function for acceleration of the car (in terms of t = t + 1). Now simply plug the values of t=0 and t=2 to find the acceleration of the car at those values of t.a) Acceleration = 1 ms^-2b) Acceleration = 3 ms^-2