A fluid flows along the \(x\) axis with a velocity given by \(\mathbf{V}=(x / t) \hat{\mathbf{i}}\), where \(x\) is in feet and \(t\) in seconds.

(a) Plot the speed for \(0 \leq x \leq 10 \mathrm{ft}\) and \(t=3 \mathrm{~s}\).

(b) Plot the speed for \(x=7 \mathrm{ft}\) and \(2 \leq t \leq 4 \mathrm{~s}\).

(c) Determine the local and convective acceleration.

(d) Show that the acceleration of any fluid particle in the flow is zero.

(e) Explain physically how the velocity of a particle in this unsteady flow remains constant throughout its motion.