Worksheet 2.5 - Rates Of Change And Particle Motion I Worksheet Page 4
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8Calculus Maximus
WS 2.5: Rates of Change & Part Mot I
8. The data in the table below gives selected values for the velocity, in meters/minute, of a particle moving
along the x-axis. The velocity v is a differentiable function of time t.
Time t (min)
0
2
5
6
8
12
( )
Velocity
v t
−
3
2
3
5
7
5
(meters/min)
t = , is the particle moving to the right or to the left? Justify.
(a) At
0
t ≤ ≤
(b) Is there a time during the time interval 0
12
minutes when the particle is at rest? Explain your
answer.
( )
( )
v ′
v ′
(c) Use data from the table to find an approximation for
and explain the meaning of
in
10
10
terms of the motion of the particle. Show the computations that lead to your answer, and indicate
units of measure.
t ≤ ≤
(d) Find the average acceleration of the particle for 8
12
min. Explain what this number means in
terms of the particle’s velocity on that interval.
( )
( )
( )
′
=
(e) Let
a t denote the acceleration of the particle at time t, such that
. Is there guaranteed
v t
a t
( )
=
t ≤ ≤
a c = ? Justify your answer.
to be a time t c
in the interval 0
12
such that
0
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