An automobile is driven on a straight road, and the distance traveled by the automobile after time t=0 is given by a quadratic function s , where s(t) is measured in feet and t is measured in seconds for 0≤t≤12 . Of the following, which gives the best estimate of the velocity of the automobile, in feet per second, at time t=8 seconds?

Question

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MrRoyal MrRoyal · Answer 1 · 2020-09-27T11:40:28+02:00

Answer:

See Explanation

Explanation:

The question is incomplete as the value of s(t) is missing;

However, the following explanation will guide you;

I'll continue my explanation with the following assumption that:

[tex]s(t) = 64 + 4(t-6)[/tex]

Required

Determine the velocity at t = 8

To do this; first calculate s(t) by substituting 8 for t in [tex]s(t) = 64 + 4(t-6)[/tex]

[tex]s(8) = 64 + 4(8- 6)[/tex]

[tex]s(8) = 64 + 4(2)[/tex]

[tex]s(8) = 64 + 8[/tex]

[tex]s(8) = 72[/tex]

Next, is to calculate the velocity by dividing s(t) by t where t = 8

i.e.

[tex]Velocity = \frac{s(t)}{t}[/tex]

Substitute 8 for t

[tex]Velocity = \frac{s(8)}{8}[/tex]

Substitute 72 for s(8)

[tex]Velocity = \frac{72}{8}[/tex]

[tex]Velocity = 9\ ft/s[/tex]

So: all you need to do is first calculate s(8), then divide the resulting value by 8 to get your result