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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 = x^{2}, 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 a_{x} (in m/s^{2}). (For example, a_{x} = 3x is a possible expression.)

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

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