AP1_Ch2studyguide

 Name _______________________________ Period _______ Date ___________

 AP Physics I: Kinematics in One Dimension

Study Guide 1. Analyzing motion with graphs.  A minivan travels al ong a straight road. It init ially starts movi ng toward the east. Below B elow is the position-time graph of the minivan. Use the information in the graph to answer the questions.

Questions 1 – 7 refer to the figure above.

1. Does the minivan move to the east? If so, during which time interval(s)?  _______________________________________________________________ 2. Does the minivan move to the west? If so, during which time interval(s)?  _______________________________________________________________ 3. Is the minivan’s speed between speed between t 2 and t 3?

t 1 and t 2 greater

than, less than, or equal to its

 _______________________________________________________________ 4. Is the minivan’s speed between t 4 and t 5 greater than, less than, or equal to its speed between t 6  and t 7 ?  _______________________________________________________________ 5. Does the minivan ever stop completely? If so, at which time(s)?  _______________________________________________________________ 6. Does the minivan ever move with a constant velocity? If so, at which time(s)?  _______________________________________________________________ 7. What is the total displacement of the minivan during the trip?  _______________________________________________________________

8. Below is the velocity-time graph of an object moving along a straight path. Use the information in the graph to fill in the table below.

9. For each of the lettered intervals below, indicate the motion of the object (whether it is speeding up, slowing down, constant velocity, or at rest), the direction of the velocity (+, !, or 0), and the magnitude and direction of the acceleration (+, !, or 0). Time interval

Motion

v

a

 A  B C  D  E

What is the total displacement of the object over the entire time interval?

2. Analyzing motion with equations. Velocity

Acceleration

Using the definitions above we obtain the following equations for motion with constant acceleration:

Practice problems: Applying the kinematic equations 1. An automobile that set the world record for acceleration increased speed from rest to 96 km/h in 3.07 s. How far had the car traveled by the time the final speed was achieved? (ans. 41 m)

2. Some tropical butterflies can reach speeds of up to 11 m/s. Suppose a butterfly flies at a speed of 6.0 m/s while another flying insect some distance ahead flies in the same direction with a constant speed . The butterfly then increases 2 its speed at a constant rate of 1.4 m/s  and catches up to the other insect 3.0 s later. How far does the butterfly travel during the race? (ans. 24 m)

3. In 1994, a human-powered submarine was designed in Boca Raton, Florida. It achieved a maximum speed of 3.06 m/s. Suppose this submarine starts from 2 rest and accelerates at 0.800 m/s  until it reaches maximum speed. The submarine then travels at constant speed for a nother 5.00 s. Calculate the total distance traveled by the submarine. (ans. 21.1 m)

4. The distance record for someone riding a motorcycle on its rear wheel without stopping is more than 320 km. Suppose the rider in this unusual situation travels with an initial speed of 8.0 m/s before speeding up. The rider then travels 40.0 m at a constant acceleration of 2.00 m/s 2. What is the rider’s speed after the acceleration? (ans. 15 m/s)

5. With a cruising speed of 2.30 " 103 km/h, the French supersonic passenger  jet Concorde is the fastest commercial airplane. Suppose the landing speed of the Concorde is 20.0 percent of the cruising speed. If the plane accelerates at !5.80 m/s2, how far does it travel between the time it lands and the time it comes to a complete stop? (ans. 1.41 km)

6. Two cars are traveling along a straight road. Car A maintains a constant speed of 80 km/h and car B maintains a constant speed of 110 km/h. At t = 0, car B is 45 km behind car A. ( a) How much farther will car A travel  before car B overtakes it? (b) How much ahead of A will B be 30 s after it overtakes A? (ans. a) 1.2 105 m b) 0.25 km)

3. Falling Objects •

If an object moves under the influence of gravity only, and no other forces, we call the resulting motion free fall.

•

Any two objects in free fall, regardless of their mass, have the same acceleration (in cases where we can neglect air resistance).

•

The symbol for this acceleration is g and its value is 9.81 m/s

2

We can rewrite the kinematic equations for the case of free fall as follows: ! y

v v

=

=

2

=

v 0 t  "

 1

g(!t )

2

2 v0  " g(!t ) 2

v 0 " 2 g! y

Practice Problems: Falling Bodies 1. The John Hancock Center in Chicago is the tallest building in the United States in which there are residential apartments. The Hancock Center is 343 m tall. Suppose a resident accidentally causes a chunk of ice to fall from the roof. What would be the velocity of the ice as it hits the ground?  Neglect air resistance. (ans. –82.0 m/s)

2. The Westin Stamford Hotel in Detroit is 228 m tall. If a worker on the roof drops a sandwich, how long does it take the sandwich to hit the ground, assuming there is no air resistance? (ans. 6.82 s)

3. A baby squirrel falls out of a nest in the tallest Sequoia tree in Redwood  National Park. 4.75 seconds elapse before it makes a dull thud when it hits the ground. How tall is the tree? (ans. 111 m)

4. A ball is launched directly upward from ground level with an initial speed of 20 m/s. (Air resistance is negligible.) ( a) How long is the ball in the air? ( b) What is the greatest height reached by the ball? ( c) How many seconds after launch is the ball 15 m above the release point? (ans. a) 4.1s b) 20m c) 0.99 s and 3.1 s)

5. A rock is thrown vertically downward from a 100 m cliff with an initial speed of 15 m/s. (a) with what speed does it reach the bottom of the cliff and b) how long does it take to get there? c) what is the position of the rock after 2 seconds? (ans. a) 47 m/s, b) 3.3 s c) 49.6 m (Neglect air resistance)