The trooper, traveling about twice as fast as the car, must swerve (ijai) EXERCISE : Suppose the driver in this example now slams on the brakes, stopping the car in 4 s. Find (a) the acceleration, (b) the distance the car travels while braking, assuming the acceleration is constant, and (c) the average velocity. ANSWERS (a) -4.38 m/s (b) 35.0 m (c) 8.75 m/s Example-2: GOAL Solve a problem involving two objects, one moving at con- stant acceleration and the other at constant velocity. a = -1.00 s ta = 0 PROBLEM A car traveling at a constant speed of 24.0 m/s passes a trooper hidden behind a billboard, as in next figure. One second after the speeding car passes the billboard, the trooper sets off in chase with a constant acceleration of 3.00 m/s. (a) How long does it take the trooper to overtake the speeding car? (b) How fast is the trooper going at that time? SOLUTION (a) How long does it take the trooper to overtake the car? Write the equation for the car's displacement: , Axar = Xar = tht + ař Take x, = 24.0 m, v, = 24.0 m/s, and acar 0. Solve + vt = 24.0 m + (24.0 m/s)t Xar= Nrite the equation for the trooper's position, taking - 0, v,= 0, and aer = 3.00 m/s: Kurooper = 4r0oper = }(3.00 m/s*) = (1.50 m/s³) Set oper=r and solve the quadratic equation. (The quadratic formula appears in Appendix A, Equation A.8.) Only the positive root is meaningful. 14 %3D (1.50 m/s)t 24.0 m + (24.0 m/s)t (1.50 m/s)12- (24.0 m/s)t- 24.0 m 0 1= 16.9 s (b) Find the trooper's speed at that time. Substitute the time into the trooper's velocity cquation: = v, + arooper = 50.7 m/s Vrooper =0 + (3.00 m/s®)(16.9 s) X voli REMARKS: equal ne and
The trooper, traveling about twice as fast as the car, must swerve (ijai) EXERCISE : Suppose the driver in this example now slams on the brakes, stopping the car in 4 s. Find (a) the acceleration, (b) the distance the car travels while braking, assuming the acceleration is constant, and (c) the average velocity. ANSWERS (a) -4.38 m/s (b) 35.0 m (c) 8.75 m/s Example-2: GOAL Solve a problem involving two objects, one moving at con- stant acceleration and the other at constant velocity. a = -1.00 s ta = 0 PROBLEM A car traveling at a constant speed of 24.0 m/s passes a trooper hidden behind a billboard, as in next figure. One second after the speeding car passes the billboard, the trooper sets off in chase with a constant acceleration of 3.00 m/s. (a) How long does it take the trooper to overtake the speeding car? (b) How fast is the trooper going at that time? SOLUTION (a) How long does it take the trooper to overtake the car? Write the equation for the car's displacement: , Axar = Xar = tht + ař Take x, = 24.0 m, v, = 24.0 m/s, and acar 0. Solve + vt = 24.0 m + (24.0 m/s)t Xar= Nrite the equation for the trooper's position, taking - 0, v,= 0, and aer = 3.00 m/s: Kurooper = 4r0oper = }(3.00 m/s*) = (1.50 m/s³) Set oper=r and solve the quadratic equation. (The quadratic formula appears in Appendix A, Equation A.8.) Only the positive root is meaningful. 14 %3D (1.50 m/s)t 24.0 m + (24.0 m/s)t (1.50 m/s)12- (24.0 m/s)t- 24.0 m 0 1= 16.9 s (b) Find the trooper's speed at that time. Substitute the time into the trooper's velocity cquation: = v, + arooper = 50.7 m/s Vrooper =0 + (3.00 m/s®)(16.9 s) X voli REMARKS: equal ne and
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Question
Transcribed Image Text:The trooper, traveling about twice as fast as the car, must swerve (ijai)
EXERCISE : Suppose the driver in this example now slams on the brakes, stopping the car in 4 s. Find (a) the acceleration,
(b) the distance the car travels while braking, assuming the acceleration is constant, and (c) the average velocity.
ANSWERS (a) -4.38 m/s (b) 35.0 m (c) 8.75 m/s
Example-2:
GOAL Solve a problem involving two objects, one moving at con-
stant acceleration and the other at constant velocity.
a = -1.00 s
ta = 0
PROBLEM A car traveling at a constant speed of 24.0 m/s passes
a trooper hidden behind a billboard, as in next figure. One second
after the speeding car passes the billboard, the trooper sets off in
chase with a constant acceleration of 3.00 m/s. (a) How long does
it take the trooper to overtake the speeding car? (b) How fast is the
trooper going at that time?
SOLUTION
(a) How long does it take the trooper to overtake the car?
Write the equation for the car's displacement: ,
Axar = Xar
= tht + ař
Take x, = 24.0 m, v, = 24.0 m/s, and acar
0. Solve
+ vt = 24.0 m + (24.0 m/s)t
Xar=
Nrite the equation for the trooper's position, taking
- 0, v,= 0, and aer = 3.00 m/s:
Kurooper = 4r0oper = }(3.00 m/s*) = (1.50 m/s³)
Set oper=r and solve the quadratic equation. (The
quadratic formula appears in Appendix A, Equation A.8.)
Only the positive root is meaningful.
14
%3D
(1.50 m/s)t 24.0 m + (24.0 m/s)t
(1.50 m/s)12- (24.0 m/s)t- 24.0 m 0
1= 16.9 s
(b) Find the trooper's speed at that time.
Substitute the time into the trooper's velocity cquation:
= v, + arooper
= 50.7 m/s
Vrooper
=0 + (3.00 m/s®)(16.9 s) X
voli
REMARKS:
equal
ne and
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