# Integration problem

#### tjrg85

##### New member
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

#### Jomo

##### Elite Member
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!

#### tjrg85

##### New member
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!
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

#### Subhotosh Khan

##### Super Moderator
Staff member
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
Where did you hide r in your derivation?

Have you looked at "completing the square" technique?

#### tjrg85

##### New member
Hello, I’ve accidentaly replaced r by d

#### Subhotosh Khan

##### Super Moderator
Staff member
Hello, I’ve accidentaly replaced r by d
Did you try "completing the square" technique?