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0593_C03_fm Page 73 Monday, May 6, 2002 2:03 PM

Kinematics of a Particle 73

P3.3.7: See Problem 3.3.6. Suppose an automobile traveling at 45 mph on a straight, level
roadway is suddenly braked so that its acceleration (or deceleration) is –µg, where µ is a
2
friction coefficient valued at 0.75 and g is the gravity acceleration (32.2 ft/sec ). Determine
the distance d traveled by the automobile before it stops and the time t that it takes to stop.

Section 3.4 Relative Velocity and Relative Acceleration
P3.4.1: See Example 3.4.1. Consider again rigid body B moving in reference frame R with
P and Q being two particles of B represented by points P and Q, as shown in Figure P3.4.1.

P
n 3 r
B
n
2
n Q
1
R
FIGURE P3.4.1
A body B with particles P and Q.
As before, let P be located relative to Q by the vector r given by:

r = 2 n − 3 n + 7 n ft
1 2 3
where n , n , and n are unit vectors fixed in B. Let the angular velocity ω and the angular
1
2
3
acceleration α of B in R be given as:
ωω= −2n + 3n − 4n rad sec
1 2 3

and

αα= 4n 1 + 6n 2 − 8n rad sec 2
3
It can be shown that the acceleration of P relative to Q in R may be expressed as:

/
R a P Q = αα × r + ω ×(ωω × r)
Assuming this to be the case and if the acceleration of Q in R is also known as –10n +
1
2
9n +12n ft/sec , find the acceleration of P relative to Q in R and the absolute acceleration
2
3
of P in R.
P3.4.2: A southbound motorist traveling at 45 mph approaches an intersection with an
east–west highway. When the motorist is 150 feet from the intersection, a traffic light
controlling southbound traffic turns red, and the motorist brakes, causing the car to decel-
2
erate at 16.1 ft/sec (.5 g). At the same time, an eastbound motorist operating a pickup
truck on the east–west highway is traveling at 35 mph and is 200 feet west of the intersection
with the north–south highway. At that point, the traffic light turns green for the pickup
operator, causing the operator to accelerate the truck at the rate of 3 mph per second.