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.
PROBLEM 11.71 (Continued)
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.
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.
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.
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.
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.
PROBLEM 11.76 (Continued)
PROBLEM 11.76 (Continued)