A student is asked to measure the acceleration of a cart on a “frictionless” inclined plane as in Figure 5.11, using an air track, a stopwatch, and a meter stick. The height of the incline is measured to be 1.774 cm, and the total length of the incline is measured to be d = 127.1 cm. Hence, the angle of inclination θ is determined from the relation sin θ = 1.774/127.1. The cart is released from rest at the top of the incline, and its position x along the incline is measured as a function of time, where x = 0 refers to the initial position of the cart. For x values of 10.0 cm, 20.0 cm, 35.0 cm, 50.0 cm, 75.0 cm, and 100 cm, the measured times at which these positions are reached (averaged over five runs) are 1.02 s, 1.53 s, 2.01 s, 2.64 s, 3.30 s, and 3.75 s, respectively. Construct a graph of x versus t2, and perform a linear least-squares fit to the data. Determine the acceleration of the cart from the slope of this graph, and compare it with the value you would get using a` = g sin θ, where g = 9.80 m/s2.

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