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4 1
12–41.
The elevator starts from rest at the first floor of the
building. It can accelerate at and then decelerate at
Determine the shortest time it takes to reach a floor
40 ft above the ground. The elevator starts from rest and
then stops. Draw the a–t,v–t, and s–tgraphs for the motion.
2ft>s2.
5ft>s2
40 ft
4 2
12–42.
The velocity of a car is plotted as shown. Determine the
total distance the car moves until it stops
Construct the a–t graph. 1t=80 s2.
10
v
(m/s)
SOLUTION
4 3
SOLUTION
12–43.
The motion of a jet plane just after landing on a runway
is described by the a–t graph. Determine the time t
′
when
the jet plane stops. Construct the v–t and s–t graphs for the
motion. Here s = 0, and v = 300 ft
>
s when t = 0.
t (s)
10
a (m/s2)
10
20 t¿
20
4 4
12–43. Continued
4 5
*12–44.
The v–tgraph for a particle moving through an electric field
from one plate to another has the shape shown in the figure.
The acceleration and deceleration that occur are constant
and both have a magnitude of If the plates are
spaced 200 mm apart, determine the maximum velocity
and the time for the particle to travel from one plate to
the other. Also draw the s–tgraph. When the
particle is at s=100 mm.
t=t¿>2
t¿
vmax
4m>s2.
SOLUTION
v
s
max
v
max
s
4 6
12–45.
SOLUTION
v
s
max
v
max
s
The v–t graph for a particle moving through an electric field
from one plate to another has the shape shown in the figure,
where t¿ = 0.2 s and vmax = 10 m>s. Draw the s–t and a–t graphs
for the particle. When t = t¿>2 the particle is at s = 0.5 m.
4 7
SOLUTION
12–46.
The a–s graph for a rocket moving along a straight track has
been experimentally determined. If the rocket starts at s = 0
when v = 0, determine its speed when it is at
s = 75 ft, and 125 ft, respectively. Use Simpson’s rule with
n = 100 to evaluate v at s = 125 ft.
s (ft)
a (ft/s2)
100
5
a 5 6(s 10)5/3
4 8
12–47.
A two-stage rocket is fired vertically from rest at s = 0 with
the acceleration as shown. After 30 s the first stage, A, burns
out and the second stage, B, ignites. Plot the v–t and s–t
graphs which describe the motion of the second stage for
0… t … 60 s.
SOLUTION
24
12
A
B
a (m/s2)
4 9
12–47. Continued
5 0
SOLUTION
*12–48.
The race car starts from rest and travels along a straight
road until it reaches a speed of 26 m
>
s in 8 s as shown on the
v–t graph. The flat part of the graph is caused by shifting
gears. Draw the a–t graph and determine the maximum
acceleration of the car. 26
14
v (m/s)
v 3.5t
v 4t 6
6
5 1
12–49.
SOLUTION
The jet car is originally traveling at a velocity of 10 m
>
s
when it is subjected to the acceleration shown. Determine
the car’s maximum velocity and the time t
′
when it stops.
When t = 0, s = 0.
6
t (s)
a (
m
/s2)
t¿
5 2
SOLUTION
12–50.
The car starts from rest at s = 0 and is subjected to an
acceleration shown by the a–s graph. Draw the v–s graph
and determine the time needed to travel 200 ft.
s (ft)
a (ft/s2)
a 0.04s 24
6
12
5 3
v
(m
/
s)
10
6
SOLUTION
12–51.
The v–t graph for a train has been experimentally
determined. From the data, construct the s–t and a–t graphs
for the motion for 0 … t … 180 s. When t = 0, s = 0.
5 4
12–51. Continued
5 5
*12–52.
A motorcycle starts from rest at s = 0 and travels along a
straight road with the speed shown by the v–t graph.
Determine the total distance the motorcycle travels until it
stops when t = 15 s. Also plot the a–t and s–t graphs.
5
10 154
t (s)
v (m/s)
v 1.25tv 5
v t 15
SOLUTION
5 6
SOLUTION
12–53.
A motorcycle starts from rest at s = 0 and travels along a
straight road with the speed shown by the v–t graph.
Determine the motorcycle’s acceleration and position when
t = 8 s and t = 12 s.
5
10 154
t (s)
v (m/s)
v 1.25tv 5
v t 15
5 7
12–54.
The v–t graph for the motion of a car as it moves along a
straight road is shown. Draw the s–t and a–t graphs. Also
determine the average speed and the distance traveled for
the 15-s time interval. When t = 0, s = 0.
SOLUTION
15
v 0.6t2
v (m/s)
5 8
12–54. Continued
5 9
12–55.
An airplane lands on the straight runway,originally traveling
at 110 ft s when If it is subjected to the decelerations
shown, determine the time needed to stop the plane and
construct the s–t graph for the motion.
t¿
s=0.>
t(s)
5
a(ft/s2)
–3
15 20 t'
–8
6 0
SOLUTION
6
8
s (ft)
a (ft/s2)
*12–56.
Starting from rest at s = 0, a boat travels in a straight line
with the acceleration shown by the a–s graph. Determine
the boat’s speed when s = 50 ft, 100 ft, and 150 ft.
