mastering physics 2
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HOMEWORK1
Due: 11:00pm on Sunday, October 28, 2012
Note: You will receive no credit for late submissions. To learn more, read your instructor's GradingPolicy
Given Positions, Find Velocity and Acceleration
Learning Goal:
To graph position, velocity, and acceleration of an object given a table of positions vs. time.
The table below shows the x coordinate of a moving object. The position is tabulated at one-secondintervals. The x coordinate is indicated below each time.
time (s) 0 1 2 3 4 5 6 7 8 9
x (m) 0 1 4 9 16 24 32 40 46 48
Part A
Which graph best represents the function , describing the object's position vs.
time?
ANSWER:
Correct
Part B
Which of the following graphs best represents the function , describing the object's velocity as a
function of time?
1
2
3
4
Hint 1. Find the velocity toward the end of the motion
The velocity is given by the slope of the displacement (position) curve. Using this fact, thevelocity toward the end of the motion is __________.
Hint 1. Finding the slope
The slope of a displacement versus time curve is given by the equation
.
ANSWER:
Hint 2. Identify the implications of zero velocity
Two of the possible velocity vs. time graphs indicate zero velocity between and .
What would the corresponding position vs. time graph look like in this region?
ANSWER:
positive and increasing
positive and decreasing
negative and increasing
negative and decreasing
a horizontal line
straight but sloping up to the right
straight but sloping down to the right
curved upward
curved downward
ANSWER:
Correct
In principle, you could also compute and plot the average velocity. The expression for the averagevelocity is
.
The notation emphasizes that this is not an instantaneous velocity, but rather an
average over an interval from to . After you compute this, you must put a single point on the
graph of velocity vs. time. The most accurate place to plot the average velocity is at the middle ofthe time interval over which the average was computed.
Part C
Which of the following graphs bestrepresents the function , describing the
acceleration of this object?
Hint 1. Find the acceleration toward the end of the motion
The acceleration is given by the slope of the velocity curve. Toward the end of the motion, whenthe velocity is decreasing, the acceleration must be __________.
Hint 1. Finding the slope
The slope of a displacement versus time curve is given by the equation
1
2
3
4
.
ANSWER:
Hint 2. Calculate the acceleration in the region of constant velocity
What is the acceleration over the interval during which the object travels at constant speed?
Express your answer numerically in meters per second per second.
ANSWER:
ANSWER:
Correct
In one dimension, a linear increase or decrease in the velocity of an object over a given timeinterval implies constant acceleration over that particular time interval. You can find the magnitudeof the acceleration using the formula for average acceleration over a time interval:
.
When the acceleration is constant over an extended interval, you can choose any value of and
within the interval to compute the average.
Problem 2.32
A person driving her car at 45 approaches an intersection just as the traffic light turns yellow. She
knows that the yellow light lasts only 2.0 before turning red, and she is 28 away from the near side of
the intersection (see the figure).
zero
positive
negative
= 0
1
2
3
4
Part A
Should she try to stop, or should she speed up to cross the intersection before the light turns red? The
intersection is 15 wide. Her car's maximum deceleration is -5.8 , whereas it can accelerate
from 45 to 65 in 6.0 . Ignore the length of her car and her reaction time.
ANSWER:
Correct
Problem 2.44
A falling stone takes 0.28 to travel past a window 2.2 tall (see the figure).
She should stop.
She should speed up.
Part A
From what height above the top of the window did the stone fall?
Express your answer using two significant figures.
ANSWER:
All attempts used; correct answer displayed
Problem 2.56
The figure is a position versus time graph for themotion of an object along the axis.
Consider the time interval from A to B.
Part A
Is the object moving in the positive or negative direction?
ANSWER:
Correct
Part B
Is the object speeding up or slowing down?
ANSWER:
= 2.1
in the positive direction
in the negative direction
Correct
Part C
Is the acceleration of the object positive or negative?
ANSWER:
Correct
Now consider the time interval from D to E.
Part D
Is the object moving in the positive or negative direction?
ANSWER:
Correct
Part E
Is the object speeding up or slowing down?
ANSWER:
speeding up
slowing down
negative
positive
in the positive direction
in the negative direction
speeding up
slowing down
Correct
Part F
Is the acceleration of the object positive or negative?
ANSWER:
Correct
Part G
Finally, answer these same three questions for the time interval from C to D.
ANSWER:
Submitted, grade pending
Problem 2.5
A rolling ball moves from = 3.2 to = -4.8 during the time from = 3.2 to = 7.0 .
Part A
What is its average velocity?
Express your answer using two significant figures.
ANSWER:
positive
negative
3693 Character(s) remaining
In the time interval from C to D; the object is not moving.In fact, the acceleration of the object is zero.
= -2.1
Correct
Problem 2.7
You are driving home from school steadily at 93 for 150 . It then begins to rain and you slow to 65
. You arrive home after driving 3 hours and 40 minutes.
Part A
How far is your hometown from school?
Express your answer using two significant figures.
ANSWER:
Correct
Part B
What was your average speed?
Express your answer using two significant figures.
ANSWER:
Correct
Problem 2.15
A bowling ball traveling with constant speed hits the pins at the end of a bowling lane 16.5 long. The
bowler hears the sound of the ball hitting the pins 2.40 after the ball is released from his hands.
Part A
What is the speed of the ball? The speed of sound is 340 .
ANSWER:
= 280
= 77
Correct
Problem 2.47
A stone is thrown vertically upward with a speed of 12.8 from the edge of a cliff 65.4 high (see the
figure).
Part A
How much later does it reach the bottom of the cliff?
ANSWER:
Answer Requested
Part B
What is its speed just before hitting?
ANSWER:
Answer Requested
= 7.02
= 5.19
= 38.0
Part C
What total distance did it travel?
ANSWER:
Correct
Problem 2.69
A stone is dropped from the roof of a high building. A second stone is dropped 1.94 later.
Part A
How far apart are the stones when the second one has reached a speed of 10.1 ?
ANSWER:
Answer Requested
Problem 2.81
A fast-food restaurant uses a conveyor belt to send the burgers through a grilling machine.
Part A
If the grilling machine is 1.4 long and the burgers require 2.1 to cook, how fast must the
conveyor belt travel?
Express your answer using two significant figures.
ANSWER:
Correct
Part B
= 82.1
= 38.0
= 0.67
If the burgers are spaced 17 apart, what is the rate of burger production (in )?
Express your answer using two significant figures.
ANSWER:
Correct
Score Summary:
Your score on this assignment is 65.8%.You received 65.83 out of a possible total of 100 points.
3.9