Question

The position of a particle is given by x(t)=4.0t^2+0.5t^3m

a. Find the instantaneous velocity at t=5.0 to 3.0sec

b. What will be the average velocity fist =5.0 and 6.0

Answer 1

(a) The instantaneous velocity is the derivative of position by time:

$$v(t)=8t+1.5t^2,\\ v(5)=77.5\text{ m/s},\\ v(3)=37.5\text{ m/s}.$$

(b) The average velocity is

$$v_\text{av}=\dfrac{x(6)-x(5)}{6-5}=75.92\text{ m/s}.$$