SOLUTION: The displacement (in feet) of a particle moving in a straight line is given by s=1/2t^2-6t+23, a)Find the average velocity over each time interval a) [4,8], b) [6,8], c) [8,10]

Question 989780: The displacement (in feet) of a particle moving in a straight line is given by s=1/2t^2-6t+23,
a)Find the average velocity over each time interval a) [4,8], b) [6,8], c) [8,10] d) [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).
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The displacement (in feet) of a particle moving in a straight line is given by s=1/2t^2-6t+23,
a)Find the average velocity over each time interval a) [4,8], b) [6,8], c) [8,10] d) [8,12]
I'll assume you mean s= (1/2)t^2 - 6t+23
Find the value of x for t = 4, 6, 8, 10 & 12.
s(4) = 7
s(8) = 7
Avg[4,8} = (7-7)/(8-4) = 0
Do the others the same way.
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b)Find the instantaneous velocity when t=8
Find the 1st derivative
s'(t) = t - 6
s'(8) = 8-6 = 2 ft/sec (assuming t is in seconds)
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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).
Plot the points on the graph, etc.
email via the TY note for help or to check your work.

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