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MasteringPhysics: Assignment Print View

Exercise 2.20The position of the front bumper of a test car under microprocessor control is given by

.

Part AFind its position at the first instant when the car has zero velocity.

ANSWER: = 2.17

Correct

Part BFind its acceleration at the first instant when the car has zero velocity.

ANSWER: = 9.60

Correct

Part CFind its position at the second instant when the car has zero velocity.

ANSWER: = 15.0

Correct

Part DFind its acceleration at the second instant when the car has zero velocity.

ANSWER: = -38.4

Correct

Part E

(1 of 24) [12/13/2010 7:13:27 PM] http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=1436365


Draw graph for the motion of the bumper between and .

ANSWER:

View Correct

Part F


ANSWER:

View Correct

Part G




ANSWER:

View All attempts used; correct answer displayed

Exercise 2.30

At a car is stopped at a traffic light. When the light turns green, the car starts to speed

up, and gains speed at a constant rate until it reaches a speed of 20 8 seconds after the light turns green. The car continues at a constant speed for 60 . Then the driver sees a red light up ahead at the next intersection, and starts slowing down at a constant rate. The car stops at the red light, 180 from where it was at .

Part A

Draw accurate graph for the motion of the car.

ANSWER:


Part B



Draw accurate graph for the motion of the car.

ANSWER:


Exercise 2.32

The figure is a graph of the acceleration of a model railroad locomotive moving on the x-axis.

Part A



Graph its velocity as functions of time if and at .

ANSWER:

View Answer Requested

Part B

Graph its x-coordinate as functions of time if and at .

ANSWER:


Exercise 2.34



A subway train starts from rest at a station and accelerates at a rate of for 14.0

. It runs at constant speed for 70.0 and slows down at a rate of until it stops at the next station.

Part AFind the total distance covered.

ANSWER: = 1.80

Correct

Exercise 2.53

The graph in the figure describes the acceleration as a function of time for a stone rolling down a hill starting from rest.

Part A

Find the change in the stone's velocity between and .

Express your answer using two significant figures.

ANSWER: = 30

Correct

Part B



Sketch a graph of the stone's velocity as a function of time.

ANSWER:


Problem 2.55

The position of a particle between and is given by

.

Part A

Draw the - graphs of this particle.

ANSWER:

View Correct

Part B




ANSWER:


Part C


ANSWER:

View Correct

Part D

At what time(s) between and is the paslyrticle instantaneou at rest?

Express your answer numerically. If there is more than one answer enter each answer separated by a comma.

ANSWER: = 0.630,1.60

Correct

Part E



At is the acceleration of the particle positive or negative?

ANSWER: positivenegative

Correct

Part F

At is the acceleration of the particle positive or negative?

ANSWER: positivenegative

Correct

Part G

At what time(s) between and is the velocity of the particle instantaneously not changing?


ANSWER: = 1.11

Correct

Part H

What is the particle's greatest distance from the origin between and

?

ANSWER: = 2.45

Correct

Part I



At what time(s) between and is the particle speeding up at the greatest rate?


ANSWER: = 2.00

Correct

Part J

At what time(s) between and is the particle slowing down at the greatest rate?


ANSWER: = 0.00×100

Correct

Problem 2.70

Two stunt drivers drive directly toward each other. At time the two cars are a distance apart, car 1 is at rest, and car 2 is moving to the left with speed . Car 1 begins to move

at , speeding up with a constant acceleration . Car 2 continues to move with a constant velocity.

Part AAt what time do the two cars collide?

ANSWER:

Correct

Part B



Find the speed of car 1 just before it collides with car 2.

ANSWER:

Correct

Test Your Understanding 2.1: Average Velocity

Part A

Rank the following trips in order of their average -velocity, from most positive to most negative. The positive -direction is to the north.

ANSWER:


Automobiles and both have average -velocity zero, since the net displacement for each trip is zero. Automobile has a net northward (positive) -displacement

in time , so

. Automobiles and both have

a net southward (negative) -displacement . For , so

; for , so

.

Test Your Understanding 2.3: Instantaneous Acceleration



The accompanying figure is an graph of the motion of a particle.

Part A

Rank the following points on the graph in order from most positive to most negative -acceleration.

ANSWER:


The concavity or curvature at a certain point on an graph shows the value of the -acceleration at that point. Hence this problem is really asking you to rank these points according to their concavity. Note that the value of or the slope of the graph does not matter. For example, at point the -acceleration is positive while is negative and the slope (equal to ) is positive; at point the -acceleration is zero while is zero and is positive; at point the -acceleration is negative while

is positive and is zero; and at point the -acceleration is zero while is



positive and is negative.

Exercise 2.50

The acceleration of a bus is given by , where = 1.18 is a constant.

Part A

If the bus's velocity at time = 1.04 is 4.97 , what is its velocity at time = 2.20 ?

ANSWER: = 7.19

Correct

Part BIf the bus's position at time = 1.04 is 6.00 , what is its position at time = 2.20 ?

ANSWER: = 12.9

Correct

Problem 2.67

Large cockroaches can attain a speed of 2.20 in short bursts. Suppose you turn on the light in a cheap motel and see one scurrying directly away from you at a constant speed 2.20 as you move toward it at a speed of 0.900 .

Part AIf you start a distance 0.880 behind it, what minimum constant acceleration would you need to catch up with it when it has traveled a distance 1.50 , just short of safety under a counter?

ANSWER: =

7.60 Answer Requested



Problem 2.65A ball starts from rest and rolls down a hill with uniform acceleration, traveling 120 during the second 6.0 of its motion.

Part AHow far did it roll during the first 6.0 of motion?


ANSWER: = 40

Correct

Multiple Choice Question - 2.30

Part AFigure 2.3

An object is moving in a straight line (the x-axis). The graph in Fig. 2.3 shows the x-coordinate of this object as a function of time. Which one of the following statements about this object is correct?



ANSWER: Between points A and B, both the x-component of its average velocity and its average speed are equal to 0.75 m/s. Between points A and B, both the x-component of its average velocity and its average speed are less than 0.75 m/s. Between points A and B, both the x-component of its average velocity and its average speed are greater than 0.75 m/s. Between points A and B, the x-component of its average velocity is 0.75 m/s, but its average speed is greater than 0.75 m/s. Between points A and B, the x-component of its average velocity is 0.75 m/s, but its average speed is less than 0.75 m/s.

Correct

Short Answer Question - 2.3

Part A

The position of an object as a function of time is given by where

, , and .

(a) Find the instantaneous acceleration at = 4.5 s. (b) Find the average acceleration over the first 4.5 seconds.

Express your answers using two significant figures separated by a comma.

ANSWER: 200,92 Answer Requested

Exercise 3.4



Part A

If , where and are positive constants, when does the velocity vector

make an angle of with the x- and y-axes?

ANSWER: =

Correct

Exercise 3.28

On your first day at work for an appliance manufacturer, you are told to figure out what to do to the period of rotation during a washer spin cycle to triple the centripetal acceleration. You impress your boss by answering immediately.

Part AWhat do you tell her?

Express your answer in terms of .

ANSWER: = 0.577 Correct

Problem 3.44

A faulty model rocket moves in the xy-plane (the positive y-direction is vertically upward). The rocket's acceleration has components and , where = 2.50

, = 9.00 , and = 1.40 . At the rocket is at the origin and has

velocity with = 1.00 and = 7.00 .

Part A



Calculate the velocity vector as a function of time.

Express your answer in terms of , , , , and . Write the vector

in the form , , where the x and y components are separated by a comma.

ANSWER: =

Correct

Part BCalculate the position vector as a function of time.

Express your answer in terms of , , , , and . Write the vector in

the form , where the x and y components are separated by a comma.

ANSWER: =

Correct

Part CWhat is the maximum height reached by the rocket?

ANSWER: = 341

Correct

Part D



Sketch the path of the rocket.

ANSWER:


Part E

What is the horizontal displacement of the rocket when it returns to ?

ANSWER: = 38.5

Correct

Problem 3.50: Spiraling Up

It is common to see birds of prey rising upward on thermals. The paths they take may be spiral-like. You can model the spiral motion as uniform circular motion combined with a constant upward velocity. Assume a bird completes a circle of radius 8.00 every 5.00 and rises vertically at a rate of 3.00 .

Part AFind the speed of the bird relative to the ground.

ANSWER: = 10.5

Correct

Part B



Find the magnitude of the bird's acceleration.

ANSWER: = 12.6

Correct

Part CFind the direction of the bird's acceleration.

ANSWER: = 0×100 Correct above the horizontal

Part DFind the angle between the bird's velocity vector and the horizontal.

ANSWER: = 16.6

Correct

Exercise 3.39

A canoe has a velocity of 0.55 southeast relative to the earth. The canoe is on a river

that is flowing 0.59 east relative to the earth.

Part AFind the magnitude of the velocity of the canoe relative to the river.


ANSWER: = 0.44 Correct

Part B



Find the direction of the velocity of the canoe relative to the river.

Express your answer as an angle measured south of west. Express your answer using two significant figures.

ANSWER: = 63 Correct south of west

Problem 3.79: Centrifuge on Mercury

A laboratory centrifuge on earth makes and produces an acceleration of 6.80 at its outer end.

Part AWhat is the acceleration (in 's) at a point halfway out to the end?

ANSWER: = 3.40

Correct

Part BThis centrifuge is now used in a space capsule on the planet Mercury, where is 0.378 what it is on earth. How many (in terms of ) should it make to produce 7

at its outer end?

ANSWER: = 0.624

Correct

Problem 3.85



In a World Cup soccer match, Juan is running due north toward the goal with a speed of 8.00 relative to the ground. A teammate passes the ball to him. The ball has a speed of 13.7

and is moving in a direction of 30.2 east of north, relative to the ground.

Part AWhat is the magnitude of the ball's velocity relative to Juan?

ANSWER: = 7.89

Correct

Part BWhat is the direction of the ball's velocity relative to Juan?

ANSWER: = 29.1 Correct north of east

Problem 3.91

For no apparent reason, a poodle is running at a constant speed of 3.30 in a circle with

radius 2.9 . Let be the velocity vector at time , and let be the velocity vector at

time . Consider and . Recall that .

Part A

For = 0.4 calculate the magnitude (to four significant figures) of the average acceleration .

Express your answer using four significant figures.

ANSWER: = 3.723

Correct

Part B



For = 0.4 calculate the direction (relative to ) of the average acceleration .

ANSWER: = 103

Correct

Part C

For = 0.2 calculate the magnitude (to four significant figures) of the average acceleration .


ANSWER: = 3.747

Correct

Part D

For = 0.2 calculate the direction (relative to ) of the average acceleration .

ANSWER: = 96.5

Correct

Part E

For = 5×10−2 calculate the magnitude (to four significant figures) of the average acceleration .


ANSWER: = 3.755

Correct

Part F



For = 5×10−2 calculate the direction (relative to ) of the average acceleration .

ANSWER: = 91.6

Correct

Part G

Compare your results to the general expression for the instantaneous acceleration for uniform circular motion that is derived in the text.

ANSWER: the magnitude of is less than of and tends to the magnitude of is greater than of and tends to

Correct

Problem 3.93

Two students are canoeing on a river. While heading upstream, they accidentally drop an empty bottle overboard. They then continue paddling for 1.2 , reaching a point 2.6 farther upstream. At this point they realize that the bottle is missing and, driven by ecological awareness, they turn around and head downstream. They catch up with and retrieve the bottle (which has been moving along with the current) 5.5 downstream from the turn-around point.

Part AAssuming a constant paddling effort throughout, how fast is the river flowing?

ANSWER: =


Part B



What would the canoe speed in a still lake be for the same paddling effort?

ANSWER: =



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