A toy cart of mass 0.50 kg moves across a horizontal table with constant acceler

Question

A toy cart of mass 0.50 kg moves across a horizontal table with constant acceleration. Its position x is measured for different times t, and the data are recorded in the table below.

(a) Calculate the average speed of the cart during each 0.50 s time interval and fill in the blank spaces in the table above.
(b) On the axes below, label the vertical axis with appropriate numbers, plot the data, and draw a best-fit line to show a graph of velocity versus time for the cart.

(c) Use the graph to calculate the acceleration of the cart.
(d) The cart continues with the constant acceleration calculated in (c) until it reaches the edge of the table at t = 3.0 s. It then falls to the floor, which is 1.2 m below the tabletop. Calculate the kinetic energy of the cart just before hitting the floor.

Explanation / Answer

(a) t = 0.5, v = ?x/?t = (0.42-0.2)/(0.5-0.0) = 0.44 m/s
t = 1.0, v = (0.9-0.42) / (1.0-0.5) = 0.96 m/s
t = 1.5, v = (1.55-0.9) / (1.5-1.0) = 1.3 m/s
t = 2.0, v = (2.3-1.55) / (2.0-1.5) = 1.5 m/s

(b) a = ?v/?t = (0.96-0.44) / 0.5 = 1.04 m/s

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