AP Physics B: Midterm Review (Kinematics)

Topics Covered in Class1.) Vector Mathematics

a. Vectors and scalarsi. A Scalar is a quantity with only a magnitude

ii. A Vector has magnitude and directionb. Additionc. Subtractiond. Multiplication

i. Dot Productii. Cross Product

2.) Kinematic variablesa. Displacment and distance (length)

i. Displacement = vectorii. Distance = scalar

b. Velocity and speed (length per unit time)i. Velocity = vector

ii. Speed = scalarc. Acceleration (length per unit time squared)

i. Both vector and scalar3.) One Dimensional Kinematics

a. Kinematic Equationsi.

ii.

iii.4.) Two Dimensional Kinematics

a. Vertical and horizontali. Motion along different axes is independent

ii. Resolve vectors into components along x and y axes using trigonometry.

b. Free fall problemsi. Acceleration due to gravity is constant

1. equals -9.8m/s2 on the surface of Earth.5.) Kinematic Graphs

a. Distance vs. time graphb. Velocity vs. time graphc. Acceleration vs. time graph (const. acceleration)

Review Questions (Easy):1.) What is the displacement of the cross-country team if they begin at the school, run

10 miles and finish back at the school?

2.) What is the distance and the displacement of the race car drivers in the Indy 500?

3.) The velocity-time graph for a two-stage rocket is shown below. Use the graph and your understanding of slope calculations to determine the acceleration and the displacement of the rocket from (a) 0 to 1.0 s, (b) 1.0 s to 4.0 s, (c) 4.0s to 12.0 s.

4.) An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the ground. Determine the distance traveled before takeoff.

5.) A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car.

6.) Upton Chuck is riding the Giant Drop at Great America. If Upton free falls for 2.6 seconds, what will be his final velocity and how far will he fall?

7.) A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration of the car and the distance traveled.

8.) A feather is dropped on the moon from a height of 1.40 meters. The acceleration of gravity on the moon is 1.67 m/s2. Determine the time for the feather to fall to the surface of the moon.

9.) Rocket-powered sleds are used to test the human response to acceleration. If a rocket-powered sled is accelerated to a speed of 444 m/s in 1.8 seconds, then what is the acceleration and what is the distance which the sled travels?

10.) A bike accelerates uniformly from rest to a speed of 7.10 m/s over a distance of 35.4 m. Determine the acceleration of the bike.

Review Questions (Difficult):

1. The nucleus of a helium atom (an alpha particle) travels along the inside of a straight hollow tube 2.0 m long which forms part of a particle accelerator.      (a). Assuming uniform acceleration, for how long is the particle in the tube if it enters

at a speed of 1.0 x 104 m/sec and leaves at 5.0 x 106 m/sec? (b). What is its acceleration during this interval?

2. The speed of an automobile traveling due east is uniformly reduced from 75.0 km/hr to 45.0 km/hr in a distance of 88.5 m.      (a). What is the magnitude and direction of the constant acceleration?      (b). How much time elapses during this deceleration?      (c). If we assume that the car continues to decelerate at the rate calculated in (a), how

much time would elapse in bringing it to rest from 75.0 km/hr?

3. Suppose I throw an eraser upward at 5.40 m/sec. How long will it take to return to my hand? How high will it go? What will its acceleration be at the top of its path? Neglect air resistance.

4. Suppose I throw an eraser at an angle of 60 degrees above the horizontal at a speed such that the upward component of the velocity is 5.40 m/s. How far will the eraser travel before returning to the height at which it was released? How high will it go?

5. It takes 1/30 s to produce a complete image on a television screen.   An electron beam travels across the screen 525 times in this time, positioning itself a little lower on the screen with each pass.  (a) How fast does the electron beam travel across a screen with a width of .5 m?  (b) If the electron beam starts at the upper left hand corner of the screen and ends at the lower right hand corner of the screen, and the television is square, what is the magnitude of its average velocity?

6. In order to make a long journey a spaceship must travel as fast as possible.   Relativity and engineering technology limit its maximum speed to about one-tenth the speed of light (the speed of light is 3x10^8 m/s).  To avoid psychological stress on the ship's occupants, the ship can accelerate at only 10 m/s^2.   (a) How many years does it take the ship to reach its maximum speed?  (b) How far does it travel in that time?  (c) Plot the position vs. time graph of the spaceship (use seconds for time).

7. A bat flying towards a wall sends out a sound wave at a distance of 2 m from the wall.  The sound wave travels at 330 m/s.  If the bat is flying at 20 m/s, how far will it travel in the time it takes for the sound wave to hit the wall and return to the bat?

8. A stampeding herd of bulls moves at a speed of 7 m/s.  A boy standing at rest 20 m in front of the bulls starts accelerating at 3 m/s^2.   Will the boy make it, i.e. will he not be

trampled?  Plot the time vs. position graphs of the boy and the bulls on the same set of axes.