Worksheet C: 1D motion
1. The following graph describes the motion of a toy train. It starts moving forwards.
a.
The speed of the train is zero at
t
=
0, 8 s and 16 s
b.
When does the train move forwards?
0 < t < 8 s (when v > 0)
c.
When does the train move backwards?
8 s < t < 16 s (when v < 0)
d.
When does the train speed up?
0 < t < 2 s ( v>0 and a>0 ) and
8 s
< t < 10 s ( v<0 and a<0 )
e.
When does the train travel at constant speed?
2 s < t < 4 s
f.
At
t
= 6 s, the acceleration is
a
=
2
0
4 m/s
1 m/s
4 s
v
a
t
∆
−
=
=
= −
∆
(slope of vt curve)
v
x
(m/s)
2
4
6
8
10
12
14
16
4
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(Worksheet C)
g.
At
t
= 8 s, the acceleration is
a
=
2
1 m/s
a
= −
(same slope)
h.
At
t
= 16 s, the instantaneous acceleration is
a
i
=
Draw the tangent line to the curve at t = 16 s. From the figure, this line goes (more or
less) through (t, v) = (16 s, 0) and (14 s, 2 m/s). Thus,
2
0
(
2) m/s
slope of tangent line
1 m/s
16 s
14 s
a
− −
=
=
=
−
i.
The average acceleration between
t
= 10 and
t
= 16 s is
a
average
=
2
average
0
(
2) m/s
0.3 m/s
16 s
10 s
v
a
t
∆
− −
=
=
=
∆
−
j.
Estimate the total displacement of the train.
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 Fall '08
 HerreraSiklody
 Acceleration, Work, Velocity, m/s

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