Problem: Frieght trains can produce only relatively small accelerations and decelerations. (a) What is the final velocity of a freight train that accelerates at a rate of 0.0500 m/s2 for 8.00 min, starting with an initial velocity of 4.00 m/s? (b) If the train can slow down at a rate of 0.550 m/s2, how long will it take to come to stop from this velocity? (c) How far will it travel in each case? 

FREE Expert Solution

The kinematics equations we may use include:

$$\begin{gathered} \boxed{\mathbf{ }{\mathbf{v}}_{\mathbf{f}}\mathbf{ }\mathbf{=}\mathbf{ }{\mathbf{v}}_{\mathbf{0}}\mathbf{ }\mathbf{+}\mathbf{a}\mathbf{t} \\ \mathbf{∆}\mathbf{x}\mathbf{=}\mathbf{ }\mathbf{\left(}\frac{{\mathbf{v}}_{\mathbf{f}}\mathbf{+}{\mathbf{v}}_{\mathbf{0}}}{\mathbf{2}}\mathbf{\right)}\mathbf{t} \\ \mathbf{∆}\mathbf{x}\mathbf{=}\mathbf{ }{\mathbf{v}}_{\mathbf{0}}\mathbf{t}\mathbf{+}\frac{1}{2}\mathbf{a}{\mathbf{t}}^{\mathbf{2}} \\ \mathbf{ }{{\mathbf{v}}_{\mathbf{f}}}^{\mathbf{2}}\mathbf{=}\mathbf{ }{{\mathbf{v}}_{\mathbf{0}}}^{\mathbf{2}}\mathbf{ }\mathbf{+}\mathbf{2}\mathbf{a}\mathbf{∆}\mathbf{x}} \end{gathered}$$