Kinematics unit test
A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.
Kinematic equation without time
Scalar vs vector
Range of a projectile
The two roots of a projectile time equation
Projectile motion independence
Independence of projectile components
A horizontal line on each motion graph means something different
Zero velocity does not mean zero acceleration
Slope of a position-time graph
Displacement vs distance
Negative area under a velocity-time graph
Slope with units
Short answer 1. Define or explain: Instantaneous velocity from a position graph
3 ptsShort answer 2. Define or explain: Average vs instantaneous velocity
3 ptsShort answer 3. Define or explain: Kinematic equation without final velocity
3 ptsShort answer 4. Define or explain: Reference frame
3 ptsFree response
10 ptsA cart is released from rest at the top of a straight track inclined at an angle θ above the horizontal. Frictional forces are negligible. A motion sensor records the cart's position x measured from its release point. t (s) 0 0.50 1.00 1.50 2.00 x (m) 0 0.60 2.40 5.40 9.60
A(i). Describe the shape of a graph of position versus time for the cart, and state what that shape indicates about the cart’s velocity.
A(ii). Calculate the average velocity of the cart over the interval from t = 0 to t = 2.00 s.
A(iii). Using the data, determine the instantaneous velocity of the cart at t = 1.00 s. Show the work that leads to your answer.
B. Derive an expression for the acceleration of the cart in terms of a measured position x and the corresponding time t, and calculate its numerical value using the data.
C. Derive an expression for the incline angle θ in terms of the acceleration a and physical constants, and calculate θ.
D. The experiment is repeated on a track that is not frictionless. Indicate whether the angle required to produce the same acceleration would be greater than, less than, or equal to your answer in part C, and justify your response.