Answer to Question #253442 in Calculus for Fahad

Question

The accompanying figure shows the position versus time curve for a certain particle moving along a straight line.

Estimate each of the following from the graph:

(a) the average velocity over the interval 0 ≤ t ≤ 3

(b) the values of t at which the instantaneous velocity is zero

(c) the values of t at which the instantaneous velocity is either a maximum or a minimum

(d) the instantaneous velocity when t = 3 s.

Answer 1

(a) the average velocity over the interval 0 ≤ t ≤ 3

$$v_{ave}=\dfrac{40m-40m}{3s-0s}=0m/s$$

(b) the values of t at which the instantaneous velocity is zero

$$s'(t)=v(t)=0$$

$$t=0s, t=2s, t=4s, t=8s$$

(c) the values of t at which the instantaneous velocity is either a maximum or a minimum

$$v'(t)=s''(t)=0$$

$$t=1s, t=3s, t=6s$$

(d) the instantaneous velocity when t = 3 s.

$$v{3}=s'(3)=slope_{t=3}=\dfrac{20m-60m}{4s-2s}=-20m/s$$