Motion in One DimensionSection 1 Preview Section 1 AccelerationAcceleration Section 2 Extra QuestionsExtra Questions

Motion in One Dimension Section 1

Preview

Section 1 Acceleration

Section 2 Extra Questions


What do you think?

• Which of the following cars is accelerating?– A car shortly after a stoplight turns green– A car approaching a red light– A car with the cruise control set at 80 km/h– A car turning a curve at a constant speed

• Based on your answers, what is your definition of acceleration?


Acceleration

• Rate of change in velocity• What are the units?

– SI Units: (m/s)/s or m/s2

– Other Units: (km/h)/s or (mi/h)/s

• Acceleration = 0 implies a constant velocity (or rest)


Classroom Practice Problem

• Find the acceleration of an amusement park ride that falls from rest to a velocity of 28 m/s downward in 3.0 s.– Answer: 9.3 m/s2 downward


Direction of Acceleration

Describe the motion of an object with

vi and a as shown to the left.

• Moving right as it speeds up

• Moving right as it slows down

• Moving left as it speeds up

• Moving left as it slows down

Vi a

+ +

+ -

- -

- +


Click below to watch the Visual Concept.

Visual Concept

Acceleration


Graphing Velocity

• The slope (rise/run) of a velocity/time graph is the acceleration.– Rise is change in v– Run is change in t

• This graph shows a constant acceleration.

• Average speed is the midpoint.

2i f

avg

v vv


Graph of v vs. t for a train

• Describe the motion at points A, B, and C.

• Answers– A: accelerating (increasing

velocity/slope) to the right– B: constant velocity to the

right– C: negative acceleration

(decreasing velocity/slope) and still moving to the right


Useful Equations

1.

2.

3.

4.

5.

2i f

avg

v vv

avg

xv

t

avg

va

t

f iv v a t

21

2ix v t a t

2 2 2f iv v a x


Classroom Practice Problems

• A bicyclist accelerates from 5.0 m/s to 16 m/s in 8.0 s. Assuming uniform acceleration, what distance does the bicyclist travel during this time interval?– Answer: 84 m

• An aircraft has a landing speed of 83.9 m/s. The landing area of an aircraft carrier is 195 m long. What is the minimum uniform acceleration required for safe landing?– Answer: -18.0 m/s2


Now what do you think?

• Which of the following cars is accelerating?– A car shortly after a stoplight turns green– A car approaching a red light– A car with the cruise control set at 80 km/h– A car turning a curve at a constant speed

• Based on your answers, what is the definition of acceleration?• How is acceleration calculated?• What are the SI units for acceleration?


What do you think?

• Observe a metal ball being dropped from rest.– Describe the motion in words.– Sketch a velocity-time graph for this motion.

• Observe the same ball being tossed vertically upward and returning to the starting point.– Describe the motion in words.– Sketch a velocity-time graph for this motion.


Graphing Free Fall

• Based on your present understanding of free fall, sketch a velocity-time graph for a ball that is tossed upward (assuming no air resistance).– Is it a straight line?– If so, what is the slope?

• Compare your predictions to the graph to the right.


Click below to watch the Visual Concept.

Visual Concept

Velocity and Acceleration of an Object at its High Point


Preview

• Multiple Choice

• Short Response

• Extended Response


Multiple Choice, continued

5. What is the squirrel’s displacement at time t = 3.0 s?

A. –6.0 mB. –2.0 m C. +0.8 m D. +2.0 m

Use the position-time graph of a squirrelrunning along a clothesline to answer

questions 5–6.



5. What is the squirrel’s displacement at time t = 3.0 s?

A. –6.0 mB. –2.0 m C. +0.8 m D. +2.0 m


questions 5–6.




questions 5–6.

6. What is the squirrel’s average velocity during the time interval between 0.0 s and 3.0 s?

F. –2.0 m/sG. –0.67 m/s H. 0.0 m/s

J. +0.53 m/s



6. What is the squirrel’s average velocity during the time interval between 0.0 s and 3.0 s?

F. –2.0 m/sG. –0.67 m/s H. 0.0 m/sJ. +0.53 m/s


questions 5–6.



7. Which of the following statements is true of acceleration?

A. Acceleration always has the same sign as displacement.B. Acceleration always has the same sign as velocity.C. The sign of acceleration depends on both the direction of motion and how the velocity is changing.D. Acceleration always has a positive sign.

•



7. Which of the following statements is true of acceleration?

A. Acceleration always has the same sign as displacement.

B. Acceleration always has the same sign as velocity.C. The sign of acceleration depends on both

the direction of motion and how the velocity is changing.D. Acceleration always has a positive sign.

•



8. A ball initially at rest rolls down a hill and has an acceleration of 3.3 m/s2. If it accelerates for 7.5 s, how far will it move during this time?

F. 12 m G. 93 mH. 120 m J. 190 m



8. A ball initially at rest rolls down a hill and has an acceleration of 3.3 m/s2. If it accelerates for 7.5 s, how far will it move during this time?

F. 12 m G. 93 mH. 120 m J. 190 m


Short Response, continued

12. For an object moving with constant negative acceleration, draw the following:

a. a graph of position vs. time

b. a graph of velocity vs. time

For both graphs, assume the object starts with a positive velocity and a positive displacement from the origin.


Short Response, continued12. For an object moving with constant negative acceleration, draw the following:

a. a graph of position vs. time

b. a graph of velocity vs. time

For both graphs, assume the object starts with a positive velocity and a positive displacement from the origin.

Answers:



13. A snowmobile travels in a straight line. The snowmobile’s initial velocity is +3.0 m/s.

a. If the snowmobile accelerates at a rate of +0.50 m/s2 for 7.0 s, what is its final velocity?

b. If the snowmobile accelerates at the rate of –0.60 m/s2 from its initial velocity of

+3.0 m/s, how long will it take to reach a complete stop?



13. A snowmobile travels in a straight line. The snowmobile’s initial velocity is +3.0 m/s.

a. If the snowmobile accelerates at a rate of +0.50 m/s2 for 7.0 s, what is its final velocity?

b. If the snowmobile accelerates at the rate of –0.60 m/s2 from its initial velocity of +3.0 m/s, how long will it take to reach a complete stop?

Answers: a. +6.5 m/s b. 5.0 s


Extended Response

14. A car moving eastward along a straight road increases its speed uniformly from 16 m/s to 32 m/s in 10.0 s.

a. What is the car’s average acceleration?

b. What is the car’s average velocity?

c. How far did the car move while accelerating?

Show all of your work for these calculations.


Extended Response

14. A car moving eastward along a straight road increases its speed uniformly from 16 m/s to 32 m/s in 10.0 s.

a. What is the car’s average acceleration?

b. What is the car’s average velocity?

c. How far did the car move while accelerating?

Answers: a. 1.6 m/s2 eastward

b. 24 m/s

c. 240 m


Extended Response, continued

15. A ball is thrown vertically upward with a speed of 25.0 m/s from a height of 2.0 m.

a. How long does it take the ball to reach its highest point?

b. How long is the ball in the air?



Extended Response, continued

15. A ball is thrown vertically upward with a speed of 25.0 m/s from a height of 2.0 m.

a. How long does it take the ball to reach its highest point?

b. How long is the ball in the air?


Answers: a. 2.55 s

b. 5.18 s

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Motion in One DimensionSection 1 Preview Section 1 AccelerationAcceleration Section 2 Extra QuestionsExtra Questions