Classical Mechanics

2.3 Worked Example - Acceleration from Position

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A runner travels along the x-axis, and at time ${\displaystyle t=0}$ is at the origin. The ${\displaystyle x}$-component of the runner’s position with respect to the origin is given by:

${\displaystyle x(t)=b{t}^2}$

where ${\displaystyle b}$ is a positive constant.

(Part a) What are the units of the constant ${\displaystyle b}$? Express your answer in terms of m for meter and s for seconds.

(Part b) Find ${\displaystyle v(t)}$, the ${\displaystyle x}$-component of the runner’s velocity as a function of time.

(Part c) Find ${\displaystyle a(t)}$, the ${\displaystyle x}$-component of the runner’s acceleration as a function of time.

(Part d) Do a plot of ${\displaystyle x(t)}$, ${\displaystyle v(t)}$ and ${\displaystyle a(t)}$ vs. time.

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