Train Stopping Time

Classical Mechanics Level 1

A train traveling at $40 \text{ m}/\text{s}$ is heading towards a station $400 \text{ m}$ away. If the train must slow down with constant deceleration $a$ into the station, how long does it take to come to a complete stop, in seconds? Answer to the nearest integer.

The answer is 20.

1 solution

Matt DeCross
May 1, 2016

If the train slows down with constant deceleration, the velocity changes linearly. The average velocity is thus half the maximum velocity, so the time required is:

$t = \frac{400 \text{ m}}{20 \text{ m}/\text{s}} = 20 \text{ s}.$

One could also derive the magnitude of the acceleration first using $0=v_0^2 + 2ad$ , and then use $v = v_0+at$ to find the time, which would obtain the same result.

@Matt DeCross Correction- U have given velocity of train to be 40m/s in question.

Saraswati Sharma - 4 years, 8 months ago

This velocity is not constant over time. The constant deceleration means that the velocity changes linearly in time, so you can take the effective velocity to be half of the maximum/initial value, which is 20 m/s as quoted above.

Matt DeCross - 4 years, 7 months ago

a =vt ? How ? Am I missing something here ?

Saraswati Sharma - 4 years, 7 months ago

@Saraswati Sharma – This is a typo which I've corrected, but it does not affect the solution in any substantial way.

Matt DeCross - 4 years, 7 months ago

Sorry I had find out acceleration but no time so t=20s

Arun G - 1 year, 10 months ago

Train Stopping Time

The answer is 20.

1 solution

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