Answer to Question #253442 in Calculus for Fahad

Question #253442

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.


1
Expert's answer
2021-10-20T01:48:41-0400



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


vave=40m40m3s0s=0m/sv_{ave}=\dfrac{40m-40m}{3s-0s}=0m/s

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


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


t=0s,t=2s,t=4s,t=8st=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)=0v'(t)=s''(t)=0

t=1s,t=3s,t=6st=1s, t=3s, t=6s



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


v3=s(3)=slopet=3=20m60m4s2s=20m/sv{3}=s'(3)=slope_{t=3}=\dfrac{20m-60m}{4s-2s}=-20m/s


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