Vertical Motion and Free Fall Video Lessons

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# Problem: 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 exttip{a}{a} = 1.4 m/s2 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?

###### FREE Expert Solution

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

A.

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

We use the kinematic equation:

vmax = v0 + atac

where vmax is the maximum velocity, v0 is the initial velocity, a is the acceleration, and tac is the elapsed time during the acceleration.

Solving and calculating for tacc:

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

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###### Problem Details

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/s2 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?