The figure shows an accelerometer, a device for measuring the horizontal acceler

Question

The figure 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. Use the following as necessary: x and g.)

b) What is the acceleration if
x = 32 cm?

Explanation / Answer

              given equation:   y = x2                                                                      velocity = v = dy /dt = 2x m/s                                    acceleration a = dv/dt = 2 m/s2                (b)   If x= 32 m   , accleration a = 2m/s2      (since it doesnot depends upon x )    

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