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CHAPTER 11
PROBLEM 11.1
A snowboarder starts from rest at the top of a double black diamond hill. As he rides down the slope, GPS
coordinates are used to determine his displacement as a function of time: x= 0.5t3 + t2 + 2t where x and t are
expressed in ft and seconds, respectively. Determine the position, velocity, and acceleration of the boarder
when t = 5 seconds.
PROBLEM 11.2
The motion of a particle is defined by the relation 32
2 9 12 10,xt t t where x and t are expressed in feet
and seconds, respectively. Determine the time, the position, and the acceleration of the particle when v 0.
PROBLEM 11.3
The vertical motion of mass A is defined by the relation 10 sin 2 15cos 2 100,xtt
where x and t are expressed in mm and seconds, respectively. Determine (a) the position,
velocity and acceleration of A when t 1 s, (b) the maximum velocity and acceleration of A.
36.056
max 36.1 mm/sv
Note that we could have also used
22
max 20 30 36.056v
by combining the sine and cosine terms.
For amax we can take the derivative and set equal to zero or just combine the sine and cosine terms.
22 2
max
40 60 72.1 mm/sa
2
max 72.1 mm/sa
PROBLEM 11.4
A loaded railroad car is rolling at a constant velocity
when it couples with a spring and dashpot bumper
system. After the coupling, the motion of the car is
defined by the relation
4.8
60 sin16
t
x
et
where x and t
are expressed in mm and seconds, respectively.
Determine the position, the velocity and the
acceleration of the railroad car when (a) t 0,
(b) t 0.3 s.
PROBLEM 11.5
The motion of a particle is defined by the relation 43 2
621233,xt t t t
where x and t are expressed in
meters and seconds, respectively. Determine the time, the position, and the velocity when 0.a
PROBLEM 11.6
The motion of a particle is defined by the relation
32
9248,xt t t
where x and t are expressed in inches
and seconds, respectively. Determine (a) when the velocity is zero, (b) the position and the total distance
traveled when the acceleration is zero.
PROBLEM 11.7
A girl operates a radio-controlled model car in a vacant
parking lot. The girl’s position is at the origin of the xy
coordinate axes, and the surface of the parking lot lies in the
x-y plane. She drives the car in a straight line so that the x
coordinate is defined by the relation x(t) = 0.5t3 - 3t2 + 3t +
2, where x and t are expressed in meters and seconds,
respectively. Determine (a) when the velocity is zero, (b)
the position and total distance travelled when the
acceleration is zero.
PROBLEM 11.8
The motion of a particle is defined by the relation
3
22,xt t where x and t are expressed in feet and
seconds, respectively. Determine (a) the two positions at which the velocity is zero, (b) the total distance
traveled by the particle from t 0 to t 4 s..
