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).
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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