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UNDERSTANDING THE VELOCITY CURVE Post-Test · To find the acceleration of the particle at a given...

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UNDERSTANDING THE VELOCITY CURVE Post-Test Developed by Sean Moroney and James Petersen The Velocity Curve in Calculus Introductory Calculus - The Velocity Curve
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Page 1: UNDERSTANDING THE VELOCITY CURVE Post-Test · To find the acceleration of the particle at a given instant, A. locate the nearest point of inflection on the velocity curve. B. determine

UNDERSTANDING THE VELOCITY CURVEPost-TestDeveloped by Sean Moroney and James Petersen

The Velocity Curve in Calculus

I n t r o d u c t o r y C a l c u l u s - T h e Ve l o c i t y C u r v e

Page 2: UNDERSTANDING THE VELOCITY CURVE Post-Test · To find the acceleration of the particle at a given instant, A. locate the nearest point of inflection on the velocity curve. B. determine

the Post-Test

Learning about the Velocity Curve

During the course of this instructional module, you have had an opportunity to gain a better understanding of the major elements of the Velocity Curve and the information you can infer about a system in motion from looking at graphs of what is happening in that system.

Application of the Velocity Curve

As you move on in Math, Physical Science, Biological Science, and the Social Sciences, you will encounter more examples and applications of the Velocity Curve concepts you have learned. You may even encounter examples of Velocity Curves in Digital Animation and Electronic Music. By having an understanding of what the Velocity Graph is telling you, you can better understand important concepts in a variety of disciplines.

Economics

AstronomyBiochemistry

Velocity Curve Post-Test

The Post-Test consists of some questions about the concepts you have learned. For the multiple-choice questions, please write the letter corresponding to the best answer to the question in the space to the left of the number.

The Velocity Curve in Calculus

I n t r o d u c t o r y C a l c u l u s - T h e Ve l o c i t y C u r v e

Page 3: UNDERSTANDING THE VELOCITY CURVE Post-Test · To find the acceleration of the particle at a given instant, A. locate the nearest point of inflection on the velocity curve. B. determine

____ 1.Whenever the velocity curve is horizontal,

A. the acceleration is about to increase.

B. the velocity is constant.

C. the particle is at its maximum displacement.

D. the particle has stopped moving.

____ 2.The area that is above a velocity curve and below the t-axis during a time interval represents

A. the minimum velocity.

B. a constant velocity.

C. the time when the acceleration is negative.

D. the net distance traveled in the negative direction during that interval.

The Velocity Curve in Calculus

I n t r o d u c t o r y C a l c u l u s - T h e Ve l o c i t y C u r v e

Page 4: UNDERSTANDING THE VELOCITY CURVE Post-Test · To find the acceleration of the particle at a given instant, A. locate the nearest point of inflection on the velocity curve. B. determine

____ 3. On the velocity curve, a point at which the acceleration changes from negative to positive is

A. a point of inflection.B. a maximum point.C. a minimum point.D. none of these.

____ 4. Motion in the negative direction is characterized by

A. the particle being in its leftmost position.B. a negative value on the velocity curve.C. negative acceleration.D. negative slope of the velocity curve.

The Velocity Curve in Calculus

I n t r o d u c t o r y C a l c u l u s - T h e Ve l o c i t y C u r v e

Page 5: UNDERSTANDING THE VELOCITY CURVE Post-Test · To find the acceleration of the particle at a given instant, A. locate the nearest point of inflection on the velocity curve. B. determine

____ 5. If the velocity of the particle, at a particular time t, is positive,

A. the particle is moving in the positive direction.B. the particle has begun to accelerate.C. the slope of the curve must also be positive.D. the particle is at a point of maximum displacement.

____ 6. When the concavity of the velocity curve is upward,

A. there is a negative net displacement.B. the particle’s acceleration is increasing.C. the particle has stopped accelerating.D. the velocity curve has a negative slope.

The Velocity Curve - Post-Test

I n t r o d u c t o r y C a l c u l u s! T h e Ve l o c i t y C u r v e

5

Page 6: UNDERSTANDING THE VELOCITY CURVE Post-Test · To find the acceleration of the particle at a given instant, A. locate the nearest point of inflection on the velocity curve. B. determine

____ 7. If the velocity curve has an upward slope at a time t, then

A. the particle has gone as far to the right as it can go.B. the velocity is positive.C. the velocity is at its maximum.D. the acceleration of the particle is positive.

____ 8. The velocity of the particle at a given instant is found

A. by determining the average concavity of the velocity curve up to that moment.B. by measuring the total area under the velocity curve.C. by determining the slope of the velocity curve at that instant.D. from its vertical coordinate on the velocity curve.

The Velocity Curve - Post-Test

I n t r o d u c t o r y C a l c u l u s! T h e Ve l o c i t y C u r v e

6

Page 7: UNDERSTANDING THE VELOCITY CURVE Post-Test · To find the acceleration of the particle at a given instant, A. locate the nearest point of inflection on the velocity curve. B. determine

____ 9. A downward slope of the velocity curve at a time t means that

A. the particle is moving at its minimum velocity.B. the velocity is decreasing at that instant.C. the particle is returning to its starting point.D. the particle is moving in the negative direction.

____ 10. On the velocity curve, a point at which the velocity changes from decreasing to increasing is

A. a maximum point.B. a point of inflection.C. a minimum point.D. none of these.

The Velocity Curve - Post-Test

I n t r o d u c t o r y C a l c u l u s! T h e Ve l o c i t y C u r v e

7

Page 8: UNDERSTANDING THE VELOCITY CURVE Post-Test · To find the acceleration of the particle at a given instant, A. locate the nearest point of inflection on the velocity curve. B. determine

____ 11. The area that is below a velocity curve and above the t-axis during an interval represents

A. the time when the acceleration is positive.B. the maximum velocity in that interval.C. the net distance covered in the positive direction during that interval.D. the region of the curve with positive slope.

____ 12. To find the acceleration of the particle at a given instant,

A. locate the nearest point of inflection on the velocity curve.B. determine the slope of the velocity curve at that instant.C. find the slope of the velocity curve at that instant.D. calculate the area under the velocity curve up to that moment.

The Velocity Curve - Post-Test

I n t r o d u c t o r y C a l c u l u s! T h e Ve l o c i t y C u r v e

8

Page 9: UNDERSTANDING THE VELOCITY CURVE Post-Test · To find the acceleration of the particle at a given instant, A. locate the nearest point of inflection on the velocity curve. B. determine

____ 13. If the slope of the velocity curve is not zero at a time t,

A. the velocity is zero.B. the velocity is changing.C. the acceleration is positive.D. the particle is about to reverse direction.

____ 14.The total displacement of a particle from its starting point, from time t = 0 to time t, is esti-

mated byA. finding the average velocity during that interval.B. calculating the average acceleration during that time.C. measuring the total area contained between the velocity curve and the t-axis.D. determining the product of the average slope and the time duration of the interval.

The Velocity Curve - Post-Test

I n t r o d u c t o r y C a l c u l u s! T h e Ve l o c i t y C u r v e

9

Page 10: UNDERSTANDING THE VELOCITY CURVE Post-Test · To find the acceleration of the particle at a given instant, A. locate the nearest point of inflection on the velocity curve. B. determine

____ 15. When a velocity curve has a straight-line portion, the particle

A. is back at its starting point.B. has stopped moving momentarily.C. has a constant acceleration.D. has an increasing velocity.

____ 16. A velocity value of zero means

A. the velocity curve at that instant is in contact with the t-axis.B. the slope of the velocity curve is zero.C. the acceleration is changing sign.D. the particle has a net displacement of zero.

The Velocity Curve - Post-Test

I n t r o d u c t o r y C a l c u l u s! T h e Ve l o c i t y C u r v e

10

Page 11: UNDERSTANDING THE VELOCITY CURVE Post-Test · To find the acceleration of the particle at a given instant, A. locate the nearest point of inflection on the velocity curve. B. determine

____ 17. A concave downward portion of the velocity curve implies that

A. the instantaneous velocity is zero.B. the slope of the velocity curve is becoming more negative.C. the acceleration is negative.D. the particle is moving in the negative direction.

____ 18. From a velocity curve, it is possible to learn

A. the velocity of the particle at all instants of time.B. the acceleration of the particle as it moves along.C. the total distance traveled by the particle through an interval of time.D. all of these.

The Velocity Curve - Post-Test

I n t r o d u c t o r y C a l c u l u s! T h e Ve l o c i t y C u r v e

11

Page 12: UNDERSTANDING THE VELOCITY CURVE Post-Test · To find the acceleration of the particle at a given instant, A. locate the nearest point of inflection on the velocity curve. B. determine

For the velocity curve in the given graph, provide a complete description of the motion of the particle. The description should include, for all parts of the motion, comments about the velocity (including both the speed and the direction), the acceleration, and the changing position (including both displacement and direction). To facilitate the description, significant points on the graph should be labeled; those labels should be used in the discussion.

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The Velocity Curve - Post-Test

I n t r o d u c t o r y C a l c u l u s! T h e Ve l o c i t y C u r v e

12


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