The function s ( t ) describes the motion of a particle along a line. s ( t ) =
ID: 2885959 • Letter: T
Question
The function
s(t)
describes the motion of a particle along a line.
s(t) = t2 7t + 5
(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.)
(c) Identify the time interval(s) in which the particle is moving in a negative direction. (Enter your answer using interval notation.)
(d) Identify the time(s) at which the particle changes direction. (Enter your answers as a comma-separated list.)
t =
Explanation / Answer
a)
V(t) =ds/dt
=d/dt(t²-7t+5)
=2t-7
b)
particle is moving in a positive direction, means V(t) >0
2t -7>0
t>7/2
interval notation is (7/2, )
c)
particle is moving in a positive direction, means V(t)<0
interval notation is (0, 7/2)
d)
t=7/2
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