FIGURE shows an accelerometer, a device for measuring the

QUESTION:

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 \(\mathrm{m}\) ) to compute the acceleration \(a_{x}\) (in \(\mathrm{m} / \mathrm{s}^{2}\) ). (For example, \(a_{x}=3 x\) is a possible expression.)

b. What is the acceleration if \(x=20 \mathrm{~cm}\) ?

Equation Transcription:

Text Transcription:

y=x^2

x

y

x

x(in m)

a_x(in m/s^2)

a_x=3x

x= 20 cm