Think It Through• How do intervals of constant acceleration appear on anacceleration-time graph?• How do intervals of constant acceleration appear on avelocity-time graph?• What does a straight-line slope indicate on an acceleration-time graph?• What would a curved line indicate on an acceleration-time graph?• Explain circumstances in which an object would beaccelerating but have an insantaneous velocity of zero?• How does uniform acceleration differ from uniform motion?Concept OrganizerThe acceleration of these sprinters willprobably be very large at first and thenlevel off to zero. Their instantaneousacceleration will not be measured andreported. You can only determine anaverage acceleration if the data takenare only the overall distance and time.What data would you need in order tocalculate instantaneous acceleration?Velocity of objectdetermined duringa number of timeintervalsUniformAccelerationNon-UniformAccelerationAverage AccelerationInstantaneousAccelerationConstant AccelerationSlope of straight lineSlope of line connectinginitial and final positionsSlope of tangent to curveThe three waYs in whichasoucan descrihe acceleration You qualitatively analyzed the motion of a vanearlier. Now, using the example of the ballthrown into the air, you can do a more detailedanalysis of the van's motion. The table shownhere includes the time and position data, withone worked example for finding acceleration.TimePositionVelocityAdAccelerationt(s)(m/s)Ar (m/s")0.00.06.02.012+3.0124.036Sample CalculationNotice that the velocity that will be plotted att = 1.0 s is the average velocity betweent = 0.0 s and t 2.0 s. The velocity that will beplotted at t 3.0 s is the average velocitybetween t = 2.0 s and 4.0 s. The accelerationthat will be plotted at t= 2.0 s is the averageacceleration between t = 1.0 s and t = 3.0s.6.0488.09610.014212.019014.022616.0250Adgd-d12 m-0.0 m2.0 s-0.0 sV =18.0262Alo2t2-lo12 m2.0 s%3DAnalyze and Conclude1. How well do the average and instantaneousvelocities that you calculated agree with= 6.0 meach other?36 m-12 mV=Afz4%3D%3D2 Separate the graphs into three sections: (a) 0 sto 8s, (b) 8 s to 12 s, and (c) 12 s to 20 s. Foreach of these three time periods, compare allthree graphs in the following ways.(a) How do the shapes of the graphs (curved,straight, horizontal) relate to each other?(b) How do the signs of the values (positive,zero, or negative) relate to each other?t4-124.0 s-2.0 s24 m2.0 s= 12 m12 -6.0 m3.0 s-1.0 s%3D%3DAt-36.0m%3D2.0 s3. Under what circumstances can the van be= 3.0 mmoving but have a zero acceleration?4. Under what circumstances is the sign ofthe velocity the same as the sign of theacceleration?Complete the table for all average velocitiesand average accelerations. Then plot position-time, velocity-time, and acceleration-timegraphs. On the position-time graph, select onepoint between 0 and 4 s and one point between6 and 10 s. Draw tangents to the curve anddetermine their slopes.5. What general statement can you make aboutthe motion of the van when the direction ofthe acceleration vector is opposite to thedirection of the velocity vector?Describing Motion • MHR65

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1. How do intervals of constant acceleration is represented on acceleration time graph. In an…

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Physics

Think It Through • How do intervals of constant acceleration appear on an acceleration-time graph? • How do intervals of constant acceleration appear on a velocity-time graph? • What does a straight-line slope indicate on an acceleration- time graph? • What would a curved line indicate on an acceleration-time graph? •Explain circumstances in which an object would be accelerating but have an instantaneous velocity of zero? • How does uniform acceleration differ from uniform motion?

Think It Through • How do intervals of constant acceleration appear on an acceleration-time graph? • How do intervals of constant acceleration appear on a velocity-time graph? • What does a straight-line slope indicate on an acceleration- time graph? • What would a curved line indicate on an acceleration-time graph? •Explain circumstances in which an object would be accelerating but have an instantaneous velocity of zero? • How does uniform acceleration differ from uniform motion?

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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Concept explainers

Displacement, Velocity and Acceleration

In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.

Linear Displacement

The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.

Topic Video

Question

Think It Through
• How do intervals of constant acceleration appear on an
acceleration-time graph?
• How do intervals of constant acceleration appear on a
velocity-time graph?
• What does a straight-line slope indicate on an acceleration-
time graph?
• What would a curved line indicate on an acceleration-time graph?
• Explain circumstances in which an object would be
accelerating but have an ins
antaneous velocity of zero?
• How does uniform acceleration differ from uniform motion?
Concept Organizer
The acceleration of these sprinters will
probably be very large at first and then
level off to zero. Their instantaneous
acceleration will not be measured and
reported. You can only determine an
average acceleration if the data taken
are only the overall distance and time.
What data would you need in order to
calculate instantaneous acceleration?
Velocity of object
determined during
a number of time
intervals
Uniform
Acceleration
Non-Uniform
Acceleration
Average Acceleration
Instantaneous
Acceleration
Constant Acceleration
Slope of straight line
Slope of line connecting
initial and final positions
Slope of tangent to curve
The three waYs in whichasoucan descrihe acceleration

You qualitatively analyzed the motion of a van
earlier. Now, using the example of the ball
thrown into the air, you can do a more detailed
analysis of the van's motion. The table shown
here includes the time and position data, with
one worked example for finding acceleration.
Time
Position
Velocity
Ad
Acceleration
t(s)
(m/s)
Ar (m/s")
0.0
0.0
6.0
2.0
12
+3.0
12
4.0
36
Sample Calculation
Notice that the velocity that will be plotted at
t = 1.0 s is the average velocity between
t = 0.0 s and t 2.0 s. The velocity that will be
plotted at t 3.0 s is the average velocity
between t = 2.0 s and 4.0 s. The acceleration
that will be plotted at t= 2.0 s is the average
acceleration between t = 1.0 s and t = 3.0s.
6.0
48
8.0
96
10.0
142
12.0
190
14.0
226
16.0
250
Adgd-d
12 m-0.0 m
2.0 s-0.0 s
V =
18.0
262
Alo2
t2-lo
12 m
2.0 s
%3D
Analyze and Conclude
1. How well do the average and instantaneous
velocities that you calculated agree with
= 6.0 m
each other?
36 m-12 m
V=
Afz4
%3D
%3D
2 Separate the graphs into three sections: (a) 0 s
to 8s, (b) 8 s to 12 s, and (c) 12 s to 20 s. For
each of these three time periods, compare all
three graphs in the following ways.
(a) How do the shapes of the graphs (curved,
straight, horizontal) relate to each other?
(b) How do the signs of the values (positive,
zero, or negative) relate to each other?
t4-12
4.0 s-2.0 s
24 m
2.0 s
= 12 m
12 -6.0 m
3.0 s-1.0 s
%3D
%3D
At-3
6.0m
%3D
2.0 s
3. Under what circumstances can the van be
= 3.0 m
moving but have a zero acceleration?
4. Under what circumstances is the sign of
the velocity the same as the sign of the
acceleration?
Complete the table for all average velocities
and average accelerations. Then plot position-
time, velocity-time, and acceleration-time
graphs. On the position-time graph, select one
point between 0 and 4 s and one point between
6 and 10 s. Draw tangents to the curve and
determine their slopes.
5. What general statement can you make about
the motion of the van when the direction of
the acceleration vector is opposite to the
direction of the velocity vector?
Describing Motion • MHR
65

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