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David S.

asked • 10/02/18

What is the acceleration?

The velocity of a train is reduced uniformly from 54.0km/h to 25.0km/h while traveling a distance of 90.0m. Compute the acceleration.

Paul M.

tutor
I think I know how to solve this but I am not sure enough to post it as an answer.  If you don't get an answer in a few hours, let me know and I will post what I think.
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10/02/18

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Arturo O. answered • 10/02/18

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Use the kinematic relation
 
v22 - v12 = 2ad ⇒
 
a = (v22 - v12) / (2d)
 
Convert speeds to m/s.
 
v2 = 25.0(1000)/3600 m/s = ? m/s
v1 = 54.0(1000)/3600 m/s = ? m/s
d = 90.0 m
 
Plug in the numbers and get acceleration in m/s2.  The negative sign just means the acceleration is opposing the direction of motion (i.e. it is slowing the vehicle down).
 
Paul, was this the approach you had in mind?
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Paul M.

tutor
No, Arturo. Thanks for doing it. I would have used an integral.
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10/02/18

Arturo O.

Paul, 
 
These problems have more than one method of solution.  For example, knowing d, v1, and v2, you could also set up a system of 2 equations in 2 unknowns a and t:
 
d = at2/2 + v1t
a = (v2 - v1)/t
 
Then solve for a and t by substitution.  But I think using the kinematic relation is the simplest solution.  Anyway, please post your solution by another method.  It may help the student see there is more than one way to attack these problems.
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10/02/18

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