In this problem, we'll consider the following kinematic equations:

$\overline{)\mathbf{}{{\mathit{v}}}_{{\mathit{f}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{+}}{\mathit{a}}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathit{x}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathit{t}}{\mathbf{+}}{\frac{1}{2}}{\mathit{a}}{{\mathit{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{\mathbf{}}{{{\mathit{v}}}_{{\mathit{f}}}}^{{\mathbf{2}}}{\mathbf{=}}{\mathbf{}}{{{\mathit{v}}}_{{\mathbf{0}}}}^{{\mathbf{2}}}{\mathbf{}}{\mathbf{+}}{\mathbf{2}}{\mathit{a}}{\mathbf{\u2206}}{\mathit{x}}}$

**A.**

Let's start by calculating the time taken to reach the maximum speed.

We use the kinematic equation:

v_{max} = v_{0} + at_{ac},

where v_{max} is the maximum velocity, v_{0} is the initial velocity, a is the acceleration, and t_{ac} is the elapsed time during the acceleration.

Solving and calculating for t_{acc}:

$\begin{array}{rcl}\mathbf{a}{\mathbf{t}}_{\mathbf{a}\mathbf{c}\mathbf{c}}& \mathbf{=}& {\mathbf{v}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\mathbf{-}{\mathbf{v}}_{\mathbf{0}}\\ {\mathbf{t}}_{\mathbf{a}\mathbf{c}\mathbf{c}}& \mathbf{=}& \frac{{\mathbf{v}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\mathbf{-}{\mathbf{v}}_{\mathbf{0}}}{\mathbf{a}}\\ & \mathbf{=}& \frac{\mathbf{6}\mathbf{.}\mathbf{1}\mathbf{-}\mathbf{0}}{\mathbf{1}\mathbf{.}\mathbf{4}}\end{array}$

A fugitive tries to hop on a freight train traveling at a constant speed of 5.1 m/s . Just as an empty box car passes him, the fugitive starts from rest and accelerates at = 1.4 m/s^{2} to his maximum speed of 6.1 m/s .

A. How long does it take him to catch up to the empty box car?

B. What is the distance traveled to reach the box car?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Vertical Motion and Free Fall concept. You can view video lessons to learn Vertical Motion and Free Fall. Or if you need more Vertical Motion and Free Fall practice, you can also practice Vertical Motion and Free Fall practice problems.

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Based on our data, we think this problem is relevant for Professor Abranyos' class at HUNTER.