Figure CP6.74 shows an accelerometer, a device for measuring the

Figure CP6.74 shows an accelerometer, a device for measuring the horizontal acceleration of cars and airplanes. A ball is free to roll on a parabolic track described by the equation y = x2, where both x and y are in meters. A scale along the bottom is used to measure the ball’s horizontal position x.

a. Find an expression that allows you to use a measured position x (in m) to compute the acceleration ax (in m/s2). (For example, ax = 3x is a possible expression.)

b. What is the acceleration if x = 20 cm?

y = x² -0.5 m 0 m 0.5 m

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