Kinematics Multiples



Velocity Graphs

From Princeton Review Book

[pic]

The following questions refer to the above velocity vs. time graph, showing the motion of a car on a straight track.

1. What is happening to the car at t = 1 second?

a. it is speeding up.

b. it is slowing down.

c. it is slowing down before t = 1 second and speeding up after t = 1 second.

d. it is speeding up before t = 1 second and slowing down after t = 1 second.

e. it is turning around.

f. none of the above.

* d---the velocity is increasing up to t = 1 and decreasing after that—it reaches a max. speed at t = 1.

2. Which of the following statements is true?

a. The car’s average velocity from t = 0 to t = 1 is less than its average velocity from t = 1 to t = 5 seconds.

b. The car’s average velocity from t = 0 to t = 1 second is the same as its average velocity from t = 1 to t = 5 seconds.

c. The car’s average velocity from t = 0 to t = 1 second is greater than its average velocity from t = 1 to t = 5 seconds.

d. Unable to determine.

* b. Since the velocity was increasing or decreasing uniformly from 0 to 20 m/s each time, the average velocity was the same: 10 m/s for each time interval.

3. In which time interval did the car travel the greatest distance (either forward or backward)?

a. from t = 0 to t = 1 second.

b. from t = 1 to t = 5 seconds.

c. from t = 5 to t = 7 seconds.

d. It is a tie between the first two time intervals.

* b. This time interval has the greatest area under the curve. Even though the first two time intervals have the same AVERAGE speed, the car spends more time traveling at this speed in the second time interval.

4. In which time interval was the magnitude of the car’s acceleration the greatest?

a. from t = 0 to t = 1 seconds.

b. from t = 1 to t = 5 seconds.

c. from t = 5 to t = 7 seconds.

d. it is a tie between the second two time intervals.

* a. The slope of the graph is the greatest in the first time interval.

5. What can you say about the car’s acceleration at t = 1 second?

a. It is positive.

b. It is negative.

c. It is undefined.

d. It is zero.

* c. The slope is undefined at a cusp.

From Old AP’s

Questions 6-8 relate to five particles that start at x = 0 at t = 0 and move in one dimension independently of one another. Graphs of the velocity of each particle versus time are shown below. (1974)

[pic]

6. Which particle is farthest from the origin at t = 2 seconds?

a. A.

b. B.

c. C.

d. D.

e. E.

*E. You are looking for the graph with the largest area under the curve.

7. Which particle moves with a constant nonzero acceleration?

a. A.

b. B.

c. C.

d. D.

e. E.

*A. Careful—these are velocity, not position graphs. Constant nonzero acceleration means velocity is non-horizontal linear function. If you chose B or E, you were thinking about acceleration graphs. If you chose D, you were thinking of position graphs.

8. Which particle is in its initial position at t = 2 seconds?

a. A.

b. B.

c. C.

d. D.

e. E.

*C. You need an equal amount of forward and backward motion—which means the total area under the curve is zero.

Questions 9 and 10 refer to the following graph:

At time t = 0 car X, traveling with speed Vo, passes car Y, which is just starting to move. Both cars then travel on two parallel lanes of the same straight road. The graphs of speed V versus time t for both cars are shown above. (1984)

9. Which of the following is true at time t = 20 seconds?

a. Car Y is behind Car X.

b. Car Y is passing Car X.

c. Car Y is in front of Car X.

d. Both cars have the same acceleration.

e. Car X is accelerating faster than Car Y.

* A. The fact that the lines intersect means that the cars have the same SPEED at this instant. However, Car X has been traveling at a constant speed while Car Y has been speeding up to match Car X’s speed. This means that Car Y must therefore have a lesser average speed than car X, which means it has not traveled as far. You also know that Car Y is behind Car X, because the area under its velocity function is less than the area under Car X’s velocity function.

10. From time t = 0 to time t= 40 seconds, the areas under both curves are equal. Therefore, which of the following is true at time t = 40 seconds?

a. Car Y is behind Car X.

b. Car Y is passing Car X.

c. Car Y is in front of Car X.

d. Both cars have the same acceleration.

e. Car X is accelerating faster than Car Y.

*B. If the areas under the curve are equal than both cars have traveled the same distance and must be in the same position.

====================================================

From Am. Journal of Physics, Vol. 62, No. 8, August 1994 (Robert J. Beichner)

11. A velocity vs. time graph for an object is shown above. When is its acceleration the most negative?

a. R to T.

b. T to V.

c. V.

d. X.

e. X to Z.

*E. The acceleration is the slope of the velocity vs. time graph. The steepest negative slope is from X to Z.

12. An elevator moves from the basement to the tenth floor of a building. The mass of the elevator is 1000 kg and it moves as shown in the velocity vs. time graph above. How far does it move during the first three seconds of motion?

a. 0.75 m.

b. 1.33 m.

c. 4.0 m.

d. 6.0 m.

e. 12.0 m.

*D. The distance traveled is the area under the curve. A = ½(base)(height) = ½(3sec)(4m/s)= 6 meters.

[pic]

13. The graph above shows the velocity as a function of time for a car of mass 1.5 x 10 3 kg. What is the acceleration of the car at t = 90 seconds?

a. 0.22 m/s2.

b. 0.33 m/s2.

c. 1.0 m/s2.

d. 9.8 m/s2.

e. 20 m/s2.

* B. The acceleration is the slope of the tangent line. The function is linear from t = 60 to t = 120 seconds.

[pic]

[pic]

14. The velocity vs. time for an airplane is shown above. At time = 65 seconds, the magnitude of the instantaneous acceleration of the object is most nearly:

a. 1 m/s2.

b. 2 m/s2.

c. 9.8 m/s2.

d. 30 m/s2.

e. 34 m/s2.

* A. The acceleration is the slope of the velocity vs. time graph. Because the function is linear in this region, we don’t have to estimate a tangent:

[pic]

15. The following represents a velocity vs. time graph for an object during a 5 second interval.

[pic]

Which one of the following graphs of acceleration vs. time would best represent the object's motion during the same time interval?

[pic]

* B

The acceleration is the derivative of the velocity.

The velocity graph has three segments: negative slope, zero slope, positive slope.

The slopes are constant, so you are looking for a step function.

16. The following represents an acceleration graph during a 5 second time interval.

Which of the following graphs of velocity vs. time would best represent the object's motion during the same time interval? Note: the magnitude of the positive acceleration (from 4 to 5) is less than the magnitude of the negative acceleration (from 1 to 3).

17. If you wanted to use the graph below to calculate the distance covered during the interval from t = 0 seconds to t = 2 seconds, you would:

[pic]

a. read 5 directly off the vertical axis.

b. find the area between that line segment and the time axis, yielding 5.

c. find the slope of that line segment by dividing 5 by 2.

d. find the slope of that line segment by dividing 15 by 5.

e. Not enough information to answer.

* B. Since velocity is the derivative of position, the distance traveled is the integral, or area under the velocity graph.

18. An object moves according to the graph below. How far does it move during the interval from t = 4 seconds to t = 8 seconds?

[pic]

a. 0.75 m.

b. 3.0 m.

c. 4.0 m.

d. 8.0 m.

e. 12.0 m.

* E.

The distance traveled is the area under the velocity vs. time graph.

Area: (1/2) (base)(height) = (1/2) ( 4 seconds) (3 m/s) = 12 m.

19. Shown below is a graph of an object's motion. Which sentence is the best interpretation?

[pic]

a. The object is moving with constant acceleration.

b. The object is moving with a uniformly decreasing acceleration.

c. The object is moving with a uniformly increasing velocity.

d. The object is moving at a constant velocity.

e. The object is not moving.

* A. Acceleration is the slope of the velocity graph.

The slope of this graph is constant.

[pic]

20. (2004, 87%)

The graph above shows velocity versus time for an object in linear motion. Which of the following is a possible graph of position, x, versus time, t, for this object?

a.

b.

c.

d.

e.

* A.

Since you are going from velocity to position, you are working backwards, or taking the integral. If you chose graph B, you were taking the derivative. The velocity graph can be broken down into three regions: in the first region, the particle moves with constant positive speed so the position graph is linear with positive slope. In the second portion, the velocity passes through zero, which means a turnaround point or a maximum on the position graph. In the third region, the particle moves with constant negative speed. This means the position graph has a constant negative slope. Also, the total area under the velocity graph is zero, which means the particle ended up where it began.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download

To fulfill the demand for quickly locating and searching documents.

It is intelligent file search solution for home and business.

Literature Lottery

Related searches