A ball is thrown vertically upward. Its height, in feet, at time t , in seconds

Question

A ball is thrown vertically upward. Its height, in feet, at time t, in seconds is given by

s(t) = -16t2 + 100.0t + 140.

What is the maximum height of the ball in feet? Round your answers to two decimal places and omit the units of measurement

A particle moves in a straight line in such a way that the position in time is given by

s(t) = t3 - 5.5t2 + 2.6t + 1.

Starting from time t = 0, when is the first time that the particle starts moving in the negative direction? Round your answers to two decimal places.

Explanation / Answer

For first part of question you should differentiate s(t) with respect to time then you will get velocity as v=ds/dt then put v=0

by this you will get t=3.125 now substitute t=3.125 in s(t) then you will get s(3.125)=296.25

For second question you should again have to differentiate with respect to time,v=0 and substitute value of t you get from there now put t=0.254 so after 0.254 sec your object will start moving in negative direction.

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