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Answer on Calculus Question for Runniel

Question #4748
4) The position function s of a particle moving along a coordinate line is given by

s(t)=4t^3 +15t^2-18t+1

, where time t is measured in minutes, and

s(t) is
measured in feet. Assume that
the positive direction extends to the right, and the negative direction extends to the

a) Determine the velocity function [rule] v(t) .

b) Determine the time intervals in which the particle moves to the right.
Use a sign chart.

c) Determine the time intervals in which the particle moves to the left.
Use a sign chart.

d) Draw a schematic representing the motion of the particle in the time interval
(-6, 3)
Expert's answer
b) particle moves to the right when v>0
12t^2+30t-18=0 when t=(-15+21)/12=1/2 or t=(-15-21)/12=-3
Hence we can say that 12t^2+30t-18>0 when t.1/2 ot t<-3
If we suppose t>0 (physically appropriate assumption) we have only one period of time t>0.5 when v>0 and hence particle moves to the right
when 0<t<0.5 particle moves to the left

d) if -6<t<3 particle moves to the left when -3<t<.5 and to the right all the rest time of the interval

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