How long would it take for a freight train to accelerate to 77.6 km/h from rest?

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Homework Help Overview

The problem involves a freight train with a specified mass and a constant force exerted by the locomotive, seeking to determine the time required to accelerate from rest to a target speed of 77.6 km/h. The context is rooted in classical mechanics, specifically focusing on concepts of force, mass, and acceleration.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between force, mass, and acceleration, questioning how to derive acceleration from the given values. There are also considerations about converting units for velocity and how that impacts the calculations.

Discussion Status

The discussion has seen participants offering guidance on breaking down the problem into steps, such as finding acceleration first and then using kinematic equations. One participant has acknowledged a mistake related to unit conversion, which has led to a recalculation of the time required.

Contextual Notes

There is an emphasis on disregarding friction in the problem setup, and the need to convert the final velocity from kilometers per hour to meters per second has been highlighted as a critical step in the calculations.

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Homework Statement



A freight train has a mass of 2.8 × 10^7 kg.
If the locomotive can exert a constant pull
of 8.1 × 10^5 N, how long would it take to
increase the speed of the train from rest to
77.6 km/h? (Disregard friction.) Answer in
units of s.

Homework Equations



F=ma

The Attempt at a Solution



I've tried everything, but I really have no clue on how to do this problem, if anyone can point me in the right direction or tell some formulas that would help it would be much appreciated.
 
Last edited:
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You know the force.

You know the mass.

So surely you have the acceleration don't you?

And if you have acceleration what it that? Isn't that the rate of change of velocity? And if you know how fast velocity is changing can't you figure how long it will take to get to that speed?
 
Do it in two steps:
(1) Find the acceleration.
(2) Use kinematics to find the time. (Convert that speed to standard units: m/s.)
 
Thanks guys I found my mistake

It was I kept finding the acceleration in m/s and never changed the final velocity from k/h to m/s

The answer was 745.13 seconds
 

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