Pre-Test Developed by Sean Moroney and James Petersen UNDERSTANDING THE VELOCITY CURVE. The Velocity Curve in Calculus

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1 in Calculus UNDERSTANDING THE VELOCITY CURVE Pre-Test Developed by Sean Moroney and James Petersen Introductory Calculus -

2 in Calculus the Pre-Test Learning about the Velocity Curve During the course of this instructional module, you will have 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 will learn. 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 Astronomy Biochemistry Velocity Curve Pre-Test This Pre-Test is intended to let you know how much you already have learned from other courses about the nature of graphs in general and about Velocity Curves in particular. This Pre-Test may also help you recall some things you might have learned previously. 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. Introductory Calculus -

3 in Calculus 1. When the particle is moving in the negative direction, A. the acceleration is negative. B. the velocity curve will have a negative slope. C. the slope of the velocity curve is negative. D. the value on the velocity curve is negative. 2. To determine the total displacement of a particle from its initial point during a specific time interval, A. the average of the initial and final velocities for that interval must be determined. B. the area between the velocity curve and the t-axis, in that interval, must be calculated. C. the total slope of the curve in that interval must be determined. D. the average slope of the curve in that interval must be determined. Introductory Calculus -

4 in Calculus 3. At times when the velocity curve is concave up, A. the particle must be moving with a relative minimum velocity. B. the net displacement must be positive. C. the acceleration is becoming more positive. D. the slope of the velocity curve must be positive. 4. A velocity curve has a negative slope during a time interval. A. the velocity during that time is increasing (becoming more positive). B. the particle has stopped accelerating. C. the particle is moving in the negative direction. D. the velocity during that time is decreasing (becoming more negative). Introductory Calculus -

5 A velocity curve is linear during a certain time interval. This implies that 5. A. the particle is at rest during that time interval. B. the acceleration is not changing during that time interval. C. the velocity is at its minimum at that time. D. the velocity curve is concave up at that time. 6. Compared with the curvature of the velocity curve around a point of inflection, the curvature around a maximum or minimum point on the velocity curve A. has the same concavity on either side. B. changes from concave up to concave down. C. is linear. D. changes from concave down to concave up. 5

6 7. The acceleration of the particle at a given instant is determined from A. the presence or absence of a point of inflection. B. the area under the velocity curve. C. the slope of the velocity curve. D. the area under the velocity curve up to that point. 8. The instantaneous velocity of the particle is determined from A. the area under the velocity curve up to that point. B. the slope of the velocity curve at that point. C. the type of concavity of the velocity curve at that point. D. its vertical coordinate on the velocity curve. 6

7 9. The area that is under a velocity curve and above the t-axis during an interval represents A. the net distance traveled in the positive direction during that interval. B. the maximum velocity in that interval. C. the region of the curve with positive slope. D. the time when the acceleration is positive. 10. When the velocity curve has a positive slope, A. the net displacement is positive. B. the particle has reached its leftmost point. C. the particle will soon have a minimum velocity. D. the particle has an acceleration in the positive direction. 7

8 11. If the particle is momentarily motionless at time t, then A. the area under the velocity curve is zero. B. the value of the velocity from the curve is zero. C. the slope of the velocity curve is changing from negative to positive. D. the particle is at its maximum displacement to the left. 12. When the particle is moving in the positive direction, A. the value on the velocity curve is positive. B. the area under the velocity curve is above the t-axis. C. the slope of the velocity curve is positive. D. the particle is near a point of inflection. 8

9 13. On the velocity curve, a point at which the acceleration changes from increasing to decreasing is A.a point of inflection. B.a maximum point. C.a minimum point. D.none of these. 14. On the velocity curve, concavity is identified A. only in regions of the curve that are straight and linear. B. only in regions of zero acceleration. C. where the graph of the velocity curve crosses the t-axis. as a consistent bending of the curve toward the upward or downward direction in a particular region. D. 9

10 15. On the velocity curve, a point at which the acceleration changes from positive to negative is A. a point of inflection. B. a minimum point. C. a point of no return. D. a maximum point. 16. During the time that the velocity curve is below the t-axis, the area between the curve and the t-axis represents A. the point of inflection of the curve. B. the maximum speed in the negative direction. C. the region of negative slope on the velocity curve. D. the net distance traveled in the negative direction during that time interval. 10

11 17. When the velocity curve is horizontal for an interval of time, then A. the total distance traveled up to that time is zero. B. the particle is at rest in that interval. C. the velocity is at its minimum value. D. the velocity is not changing in that interval. 18. A graph of velocity vs. time can provide information on A. the speed and direction of the particle at any instant. B. the location of the particle relative to its starting point. C. the rate of change of a varying velocity. D. all of these. 11

12 19. The vertical position of a point on the velocity curve relative to the t-axis A. identifies the direction in which the particle is moving. B. indicates the speed of the particle. C. indicates both the speed and the direction of the particle. D. indicates whether the particle is changing direction. 20. When the concavity of the velocity curve is facing downward, A. the acceleration is becoming more negative. B. the net displacement up to that time must be negative. C. the particle is turning around. D. the graph of the velocity curve is horizontal. 12

13 21. Whenever the slope of the velocity curve is not equal to zero, we may assume that A. the velocity is changing. B. the particle is at rest. C. the acceleration is zero. D. the particle has returned to its starting point. 22. The slope of a velocity curve at a particular point is important because it indicates A. the type of change the velocity may be undergoing. B. that the acceleration is constant. C. that the maximum displacement has been reached. D. the instantaneous value of the velocity. 13