In an experiment to estimate the acceleration of an object

Chapter 8, Problem 19E

(choose chapter or problem)

In an experiment to estimate the acceleration of an object down an inclined plane, the object is released and its distance in meters \((y)\) from the top of the plane is measured every 0.1 second from time \(t=0.1\) to \(t=1.0\). The data are presented in the following table.

The data follow the quadratic model \(y=\beta_{0}+\beta_{1} t+\beta_{2} t^{2}+\varepsilon\), where \(\beta_{0}\) represents the initial position of the object, \(\beta_{1}\) represents the initial velocity of the object, and \(\beta_{2}=a / 2\), where a is the acceleration of the object, assumed to be constant. In a perfect experiment, both the position and velocity of the object would be zero at time 0. However, due to experimental error, it is possible that the position and velocity at \(t=0\) are nonzero.

a. Fit the quadratic model \(y=\beta_{0}+\beta_{1} t+\beta_{2} t^{2}+\varepsilon\).

b. Find a 95% confidence interval for \(\beta_{2}\).

c. Find a 95% confidence interval for the acceleration a.

d. Compute the P-value for each coefficient.

e. Can you conclude that the initial position was not zero? Explain.

f. Can you conclude that the initial velocity was not zero? Explain.

Equation Transcription:

Text Transcription:

(y)

t=0.1

t=1.0

y=beta_0+beta_1t+beta_2t^2+varepsilon

beta_0

beta_1

beta_2=a/2

t=0

y=beta_0+beta_1t+beta_2t^2+varepsilon

beta_2