The function s ( t ) describes the motion of a particle along a line. s ( t ) =
ID: 2893318 • Letter: T
Question
The function s(t) describes the motion of a particle along a line.
s(t) = t3 13t2 + 16t 240
(a) Find the velocity function v(t) of the particle at any time t 0.
v(t) = _______________
(b) Identify the time interval(s) in which the particle is moving in a positive direction. (Enter your answer using interval notation.)
Answer:_____________
(c) Identify the time interval(s) in which the particle is moving in a negative direction. (Enter your answer using interval notation.)
Answer:__________________
(d) Identify the time(s) at which the particle changes direction. (Enter your answers as a comma-separated list.)
t = ___________________________
Explanation / Answer
A.
S(t) = t^3 - 13t^2 + 16t - 240
V = dS/dt
V = d(t^3 - 13t^2 + 16t - 240)/dt
V(t) = 3t^2 - 26t + 16
B.
when V(t) > 0, then particle will be moving in positive direction
V(t) = 3t^2 - 26t + 16 > 0
3t^2 - 24t - 2t + 16 > 0
(3t - 2)*(t - 8) > 0
when 0 < t < 2/3, V(t) > 0, So in this interval velocity will be in positive direction.
when t > 8, V(t) > 0, So in this interval velocity will be in positive direction.
C.
When V(t) < 0
for 2/3 < t < 8, V(t) < 0, So velocity will be in negative direction in this interval.
D.
when t = 0, particle changes direction,
at t = 2/3 sec and t = 8 sec Particle changes direction.
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