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AP Physics Kinematics in Two Dimensions

Free Response Problems

  1. A student moves a marker over the surface of a smart board. The position of the marker is given in terms of unit vectors = + (0.5 m/s)t.
  2. Find the magnitude and direction of the average velocity of the marker between t = 0 and t = 3 s.
  3. Find the magnitude and direction of the instantaneous velocity of the marker at t =0, t = 3 s, t = 5 s.
  4. Find the magnitude and the direction of the instantaneous acceleration of the marker at t = 5 s. Does the acceleration change with time?
  5. Sketch the marker’s trajectory from t = 0 to t = 5 s.
  1. The displacement of a moving object is presented by the formula = αt2 + βt3, where α =0.8 m/s2, β = 0.01 m/s3.
  2. Find the magnitude and direction of the average velocity between t = 0 and t = 4 s.
  3. Find the magnitude and direction of the instantaneous velocity at t = 2 s, t = 5 s, t = 7 s.
  4. Find the magnitude and direction of the instantaneous acceleration at t = 1 s, t = 3 s, t = 5 s.
  5. What is the angle between two vectors – velocity and acceleration at t = 5 s.
  1. A toy boat moves on the surface of a pond. The position as a function of time is given by the following formulas: x(t) = 2.6 (m/s) t and y(t) = 5 m – 1.4 (m/s2)t2.
  2. Sketch the path of the toy between t = 0 and t = 4 s.
  3. Calculate the velocity and acceleration of the toy as functions of time.
  4. Calculate the magnitude and direction of the toy’s velocity and acceleration at t = 3 s.
  5. What is the angle between two vectors – velocity and acceleration at t =3 s.
  1. A group of physics students performs an experiment with a small rocket. The rocket’s acceleration has components ax = (2.4 m/s4)t2 and ay = 8 m/s2 – (1.5 m/s3)t. At time t=0, o= 0, and o = 0.
  2. Calculate the velocity as a function of time.
  3. Calculate the position as a function of time.
  4. Calculate the maximum height reached by the rocket.
  5. Calculate the horizontal displacement of the rocket when it returns to y = 0.
  1. An air plane flies at a constant horizontal speed of 170 m/s. When the air plane is 1150 m above the ground level a pilot drops a package.
  2. How long it will take the package to reach the ground?
  3. How far horizontally will the package fly until it strikes the ground?
  4. What is the velocity of the package just before it strikes the ground?
  5. How would you compare the velocity of the package and the velocity of an object dropped from the same height 1150 m.
  1. A military jet flies horizontally with a velocity of 450 m/s and 20,000 m above the ground. When the jet is straight above an artillery gun a shell is fired. Assuming the shell hits the jet.
  2. Calculate the horizontal component of the initial velocity of the shell.
  3. Calculate the vertical component of the initial velocity of the shell.
  4. Calculate the magnitude of the initial velocity of the shell.
  5. Calculate the angle of the initial velocity above the horizontal.
  1. A ball falls on the inclined surface from the distance H. The inclined surface makes 30˚ with the horizontal. The ball strikes the surface elastically. Assuming the surface is long enough that the ball can fall on it for the second time.
  2. Find the distance along the inclined surface between the first and second collisions of the ball with the inclined.
  3. If the angle is increased to 45 ˚, what is the new distance between the first and the second collisions of the ball with the inclined?

Answer Key:

  1. A. = 1.01 m/s, = 29.1˚

B. = 0.5 m/s & = 90˚, = 1.87 m/s & = 15.51, = 3.04 m/s & = 9.46

C. = 0.6 in +x direction

D.

  1. A. = 3.2 m/s, = 2.9

B. = 3.2 m/s & = 2.15, = 8.04 m/s & = 5.36, = 11.3 m/s & = 7.48

C. = 1.6 = 2.15, = 1.61 = 6.42, = 1.63 = 10.62

D. 5.26˚

  1. A.

B. v = , a =

C. v = 8.55 m/s & =287.2, a = 2.8 = 270

D. 17.2

  1. A. v =

B. x =

C. 151.7 m

D. 13107.2 m

  1. A. 15.32s

B. 2604.4m

C. 226.81m/s

D. The package has greater velocity.

  1. A. 450m/s

B. 626.1m/s

C. 771.1m/s

D. 54.3˚

  1. A. 4H

B. 4H