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#16t^2

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Answer 1 · 2017-09-03T20:05:24

(a) $80$ $"ft/sec"$
(b) $160$ $"ft/sec"$

Average speed is given by:

$barv=(Deltax)/(Deltat)$

Here, $Deltax$ is the change in position, or $s(5)-s(0)$ feet.
$Deltat$ is $5-0$ seconds.

$barv=(s(5)-s(0))/(5-0)$ $"ft/sec"$

$color(white)barv=(16*25-16*0)/5$ $"ft/sec"$

$color(white)barv=80$ $"ft/sec"$

To find the instantaneous velocity at $t=5$ , we need to differentiate $s$ to find $v$ .

$v=(ds)/dt=d/dt16t^2=32t$

Thus, at $t=5$ :

$v=32*5=160$ $"ft/sec"$