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:
\(\displaystyle x(t)=bt^2 \)
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.