The displacement (in feet) of a particle moving in a straight line is given by s = 1 2 t 2 − 6 t + 23 , where t is measured in seconds. (a) Find the average velocity over each time interval: (i) [4, 8] (ii) [6, 8] (iii) [8, 10] (iv) [8, 12] (b) Find the instantaneous velocity when. t = 8 . (c) Draw the graph of s as a function of t and draw the secant lines whose slopes are the average velocities in part (a). Then draw the tangent line whose slope is the instantaneous velocity in part (b).
Solution Summary: The author explains how to calculate the average velocity over a time interval.
The displacement (in feet) of a particle moving in a straight line is given by
s
=
1
2
t
2
−
6
t
+
23
, where t is measured in seconds.
(a) Find the average velocity over each time interval:
(i) [4, 8]
(ii) [6, 8]
(iii) [8, 10]
(iv) [8, 12]
(b) Find the instantaneous velocity when.
t
=
8
.
(c) Draw the graph of s as a function of t and draw the secant lines whose slopes are the average velocities in part (a). Then draw the tangent line whose slope is the instantaneous velocity in part (b).
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