Question

Suppose the velocity(v) of a car at any time(t) is given by the equation v=60m/s + (0.50m/s3)t2(2 points)

A.) Derive the expression for the instantaneous acceleration at any given time.

B.) Use the derived equation to find the instantaneous acceleration at t=3s

Answer 1

(a) The acceleration is the derivative of the speed of the car with respect to time:

$$a=\dfrac{dv}{dt}=\dfrac{d}{dt}(60+0.5t^2)=t.$$

(b) The instantaneous acceleration at time $t=3\ s$:

$$a(t=3\ s)=3\ \dfrac{m}{s^2}.$$