PROBLEM 11.77
An accelerometer record for the motion of a given part of a
mechanism is approximated by an arc of a parabola for 0.2 s and a
straight line for the next 0.2 s as shown in the figure. Knowing that
0v
when 0t
and x 0.8 ft when t 0.4 s, (a) construct the vt
curve for 0
t
0.4 s, (b) determine the position of the part at t
0.3 s and t 0.2 s.
PROBLEM 11.78
A car is traveling at a constant speed of
54 km/h when its driver sees a child run into
the road. The driver applies her brakes until
the child returns to the sidewalk and then
accelerates to resume her original speed of
54 km/h; the acceleration record of the car is
shown in the figure. Assuming
0x
when
t
0,
determine (a) the time t
1
at which the
velocity is again 54 km/h, (b) the position of
the car at that time, (c) the average velocity of
the car during the interval 1
1
s.tt
PROBLEM 11.78 (Continued)
PROBLEM 11.79
An airport shuttle train travels between two terminals that are 1.6 mi apart. To maintain passenger comfort,
the acceleration of the train is limited to 4 ft/s
2
, and the jerk, or rate of change of acceleration, is limited to
0.8 ft/s
2
per second. If the shuttle has a maximum speed of 20 mi/h, determine (a) the shortest time for the
shuttle to travel between the two terminals, (b) the corresponding average velocity of the shuttle.
PROBLEM 11.79 (Continued)
PROBLEM 11.80
During a manufacturing process, a conveyor belt starts from rest and travels a total of 1.2 ft before
temporarily coming to rest. Knowing that the jerk, or rate of change of acceleration, is limited to 4.8 ft/s
2
per
second, determine (a) the shortest time required for the belt to move 1.2 ft, (b) the maximum and average
values of the velocity of the belt during that time.
PROBLEM 11.80 (Continued)
PROBLEM 11.81
Two seconds are required to bring the piston
rod of an air cylinder to rest; the acceleration
record of the piston rod during the 2 s is as
shown. Determine by approximate means (a)
the initial velocity of the piston rod, (b) the
distance traveled by the piston rod as it is
brought to rest.
PROBLEM 11.81 (Continued)
PROBLEM 11.82
The acceleration record shown was obtained
during the speed trials of a sports car.
Knowing that the car starts from rest,
determine by approximate means (a) the
velocity of the car at t 8 s, (b) the distance
the car has traveled at t 20 s.