Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
PROBLEM 11.64 (Continued)
20 300
Problem 11.65
A particle moves in a straight line with the velocity shown in the
figure. Knowing that x = –
48 ft at t = 0, draw the a–t and x–t
curves for 0 < t < 40 s and determine (a) the maximum value of
the position coordinate of the particle, (b) the values of t for
which the particle is at a distance of 108 ft from the origin.
SOLUTION
Points on the x–t curve may be calculated using areas of the v–t curve.
40 30 5
PROBLEM 11.65 (Continued)
PROBLEM 11.66
A parachutist is in free fall at a rate of 200 km/h when he opens his parachute at
an altitude of 600 m. Following a rapid and constant deceleration, he then
descends at a constant rate of 50 km/h from 586 m to 30 m, where he maneuvers
the parachute into the wind to further slow his descent. Knowing that the
parachutist lands with a negligible downward velocity, determine (a) the time
required for the parachutist to land after opening his parachute, (b) the initial
deceleration.
SOLUTION
Assume second deceleration is constant. Also, note that
PROBLEM 11.66 (Continued)
initial
PROBLEM 11.67
A commuter train traveling at 40
mi/h is 3 mi from a station. The
train then decelerates so that its
speed is 20 mi/h when it is 0.5 mi
from the station. Knowing that the
train arrives at the station 7.5 min
after beginning to decelerate and
assuming constant decelerations,
determine (a) the time required for
the train to travel the first 2.5 mi,
(b) the speed of the train as it
arrives at the station, (c) the final
constant deceleration of the train.
SOLUTION
final
PROBLEM 11.68
A temperature sensor is attached to slider AB which moves
back and forth through 60 in. The maximum velocities of the
slider are 12 in./s to the right and 30 in./s to the left. When the
slider is moving to the right, it accelerates and decelerates at a
constant rate of 6 in./s
2
; when moving to the left, the slider
accelerates and decelerates at a constant rate of 20 in./s
2
.
Determine the time required for the slider to complete a full
cycle, and construct the v – t and
xt
curves of its motion.
SOLUTION
10.5
PROBLEM 11.69
In a water-tank test involving the launching of a small model
boat, the model’s initial horizontal velocity is 6 m/s, and its
horizontal acceleration varies linearly from
2
12 m/s
at 0t
to
2
2 m/s
at t
1
t
and then remains equal to
2
2 m/s
until
1.4 s.t Knowing that 1.8 m/sv when
1
,tt
determine
(a) the value of
1
,t
(b) the velocity and the position of the
model at 1.4 s.t
SOLUTION
PROBLEM 11.69 (Continued)
50 12
vt
PROBLEM 11.70
The acceleration record shown was obtained for a small
airplane traveling along a straight course. Knowing that
x
0
and 60 m/sv when
0,t
determine (a) the velocity and
position of the plane at
20 s,t
(b) its average velocity
during the interval 6 s 14 s.t
SOLUTION
average
8 s
PROBLEM 11.71
In a 400-m race, runner A reaches her maximum velocity
A
v in
4 s with constant acceleration and maintains that velocity until
she reaches the half-way point with a split time of 25 s. Runner
B reaches her maximum velocity
B
v in 5 s with constant
acceleration and maintains that velocity until she reaches the
half-way point with a split time of 25.2 s. Both runners then
run the second half of the race with the same constant
deceleration of 0.1 2
m/s . Determine (a) the race times for both
runners, (b) the position of the winner relative to the loser
when the winner reaches the finish line.
SOLUTION
PROBLEM 11.71 (Continued)
2
PROBLEM 11.72
A car and a truck are both traveling at the
constant speed of
35 mi/h;
the car is 40 ft
behind the truck. The driver of the car
wants to pass the truck, i.e., he wishes to
place his car at B, 40 ft in front of the truck,
and then resume the speed of
35 mi/h.
The
maximum acceleration of the car is
2
5 ft/s
and the maximum deceleration obtained by
applying the brakes is
2
20 ft/s .
What is the
shortest time in which the driver of the car
can complete the passing operation if he
does not at any time exceed a speed of
50 mi/h?
Draw the
vt
curve.
m
1(22)(4.4) 48.4 ft
total 1 2 3
B
PROBLEM 11.73
Solve Problem 11.72, assuming that the driver of the car does not pay any attention to the speed limit while
passing and concentrates on reaching position B and resuming a speed of 35 mi/h in the shortest possible time.
What is the maximum speed reached? Draw the
vt
curve.
PROBLEM 11.72
A car and a truck are both traveling at the constant speed of
35 mi/h;
the car is 40 ft
behind the truck. The driver of the car wants to pass the truck, i.e., he wishes to place his car at B, 40 ft in
front of the truck, and then resume the speed of
35 mi/h.
The maximum acceleration of the car is
2
5 ft/s
and
the maximum deceleration obtained by applying the brakes is
2
20 ft/s .
What is the shortest time in which the
driver of the car can complete the passing operation if he does not at any time exceed a speed of
50 mi/h?
Draw the
vt
curve.
SOLUTION
1
total
m
m
PROBLEM 11.74
Car A is traveling on a highway at a
constant speed
0
( ) 60 mi/h,
A
v
and is 380 ft from the entrance of
an access ramp when car B enters
the acceleration lane at that point
at a speed
0
() 15 mi/h.
B
v
Car B
accelerates uniformly and enters
the main traffic lane after traveling
200 ft in 5 s. It then continues to
accelerate at the same rate until it
reaches a speed of
60 mi/h,
which
it then maintains. Determine the
final distance between the two
cars.
SOLUTION
/
BA
PROBLEM 11.75
An elevator starts from rest and moves upward, accelerating at a rate of 1.2 m/s
2
until it reaches a speed of 7.8 m/s, which it then maintains. Two seconds after the
elevator begins to move, a man standing 12 m above the initial position of the top of
the elevator throws a ball upward with an initial velocity of 20 m/s. Determine when
the ball will hit the elevator.
SOLUTION
2
PROBLEM 11.75 (Continued)
PROBLEM 11.76
Car A is traveling at 40 mi/h when it
enters a 30 mi/h speed zone. The driver
of car A decelerates at a rate of 16 ft/s
2
until reaching a speed of 30 mi/h, which
she then maintains. When car B, which
was initially 60 ft behind car A and
traveling at a constant speed of 45 mi/h,
enters the speed zone, its driver
decelerates at a rate of 20 ft/s
2
until
reaching a speed of 28 mi/h. Knowing
that the driver of car B maintains a speed
of 28 mi/h, determine (a) the closest that
car B comes to car A, (b) the time at
which car A is 70 ft in front of car B.
2
B
PROBLEM 11.76 (Continued)
() ()
AA
vv
2
B
Car B will continue to overtake car A while .
BA
vv Therefore, /min
()
AB
x will occur when ,
A
B
vv
PROBLEM 11.76 (Continued)
