Question

A fugitive tries to hop on a freight train traveling at a constant speed of 5.0 m/s. Just as an empty box car passes him, the fugitive starts from rest and accelerates at a = 4.2 m/s2 to his maximum speed of 8.0 m/s. (a) How long does it take him to catch up to the empty box car? s (b) What is the distance traveled to reach the box car? m

Answer 1

The first thing we need to do is figure out how long it took the fugitive to reach his max speed of 8 m/s. The equation we'll use to solve this is \[8.0 \frac {m}{s} = 4.2 \frac {m}{s^2} * t_0 \]Once we know how long it took the fugitive to reach maximum speed, which we will call \[t_0\]we need to figure out when the distance that the boxcar traveled is equal to the distance that the fugitive traveled. This will give us our answer to (a). The equations we will use are \[\Delta x_{car} = 5.0 \frac {m}{s} * t\]\[\Delta x_{fugitive} = \frac {1}{2} * 4.2 \frac {m}{s^2} * t_0^2 + 8.0 \frac {m}{s} * (t-t_0) \] Setting these two equations equal to each other and solving for t will give us our solution to (a).

From there, we still need to calculate the distance traveled to reach the box car. This can be solved by plugging in our value of t calculated in (a) into either our equation for the distance the box car traveled, or our equation for the distance that the fugitive traveled and solving. Since this distance is the same in both, whichever equation you use should result in the same answer.