Answer to Question #253716 in Calculus for johnwick

Question

Question 01

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

Assuming the above is the graph,

a) $v_{av} (0 ≤ t ≤ 3) = \dfrac{x_2-x_1}{t_2-t_1} = \dfrac{8-0}{3-0} = 2.67\ m/s$

b) the value of t for which the instantaneous velocity is zero is 4 ≤ t ≤ 5 because at that period there is no change in distance.

c) there is maximum instantaneous velocity when the slope is highest (which is 0 ≤ t ≤ 2) and minimum instantaneous velocity when the slope is lowest (4 ≤ t ≤ 5, instantaneous velocity is 0 at this point)

d) $v = d/t = 8/3 = 2.67\ m/s$