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A runaway train car that has a mass of 15,000 kg travels at a speed of $5.4 \textrm{ m/s}$ down a track. Compute the time required for a force of 1500 N to bring the car to rest.
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Final Answer

$54 \textrm{ s}$

Solution Video

OpenStax College Physics Solution, Chapter 8, Problem 5 (Problems & Exercises) (1:45)

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Video Transcript

This is College Physics Answers with Shaun Dychko. This train is initially moving to the right which we'll take to be the positive direction, at a speed of 5.4 meters per second. It has a mass of 15 thousand kilograms and it's going to be brought to a stop, so the final momentum will be zero. There is going to be some applied force here opposing the direction of motion which will bring it to a stop. We have to figure out how long will the force take to bring the train to a stop given that the force is 1500 Newtons. So, let's write that down on there. The change in momentum is the final minus the initial momentum and the change in momentum also has a name impulse which is net force multiplied by the time that force is acting. So we can substitute net force in place of <i>delta p</i> here in this line. So net force times time equals the final momentum minus the initial momentum. We'll solve for <i>t</i> by dividing both sides by net force and we get the time is the difference in momenta divided by net force. The initial momentum we'll calculate by multiplying the mass by the initial velocity and so we have zero minus 15 thousand kilograms times 5.4 meters per second initial velocity, all divided by negative 1500 Newtons. I have a negative there because this applied force is the net force because there is only one force and so it turns out to be the net force in this case. It is pointing in the negative direction. So I put negative 1500 Newtons there and we get 54 seconds is the time for this force to bring the train to a stop.