Integration problem

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tjrg85

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May 22, 2020
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Hello, I am learning calculus and I recently encountered this problem which I have no idea how to solve. This is the problem word for word:

A subway train travels over a distance s in t seconds. It starts from rest (zero velocity) and ends at rest. In the first part of its journey it moves with constant acceleration f and in second part with constant deceleration (negative acceleration) r. Show that [fr/(f+r)]t^2/2
 
Can you draw a graph of the movement of the train, or maybe draw a graph of the velocity of the train. You have to do something. In this forum we expect you to solve your own problem--with our help.

What does [fr/(f+r)]t^2/2 mean? Is it a distance, a velocity, something else? Look at the units and you'll get the answer!
 
Jomo said:
Can you draw a graph of the movement of the train, or maybe draw a graph of the velocity of the train. You have to do something. In this forum we expect you to solve your own problem--with our help.

What does [fr/(f+r)]t^2/2 mean? Is it a distance, a velocity, something else? Look at the units and you'll get the answer!
Click to expand...
I can draw the graph, and I managed to create this formula s=(f/2)*t1^2+f*t1*t2+(d/2)*t2^2, t1 being the time at which the train starts decelerating and t2 being the time at which the train stops (time since starting to decelerate), and I also know that at time t2 -> f*t1+d*t2=0 , but I am unable to create a formula with t and without t1 and t2
 
tjrg85 said:
I can draw the graph, and I managed to create this formula s=(f/2)*t1^2+f*t1*t2+(d/2)*t2^2, t1 being the time at which the train starts decelerating and t2 being the time at which the train stops (time since starting to decelerate), and I also know that at time t2 -> f*t1+d*t2=0 , but I am unable to create a formula with t and without t1 and t2
Click to expand...
Where did you hide r in your derivation?

Have you looked at "completing the square" technique?
 
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