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An automobile is driven on a straight road, andthe distance traveled by the automobile aftertime t= 0 is given by the quadratic functionS, where s(t) is measured in feet and t ismeasured in seconds for 0 < t < 12. Of thefollowing, which gives the best estimate of thevelocity of the car, in feet per second, at timet=8?

An automobile is driven on a straight road andthe distance traveled by the automobile aftertime t 0 is given by the quadratic functionS where st is measured in class=

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Answer:

The correct answer is the second option:

[tex]\frac{s(10)-s(6)}{10-6}[/tex]

Explanation:

The instantaneous velocity in a point is the slope of the line of the trajectory in that point.

The second option is the slope of the line of the points (6, s(6)) and (10, s(10)) and the point of interest (t = 0) is in the middle of those two points:

[tex]\frac{6+10}{2}=\frac{16}{2}=8[/tex]

Thus, this is the best estimate from the options given.,

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