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M1 speed-time graph

A train starts from rest at station A and accelerates uniformly at 3x ms^-2 until it reaches a speed of 30ms^-2. It is at constant speed for T seconds. The train then decelerates uniformly at x ms ^-2 until it comes to rest at station B. The distance between the stations is 6 km and the time taken from A to B is 5 minutes (300s).
(c)Find T and X
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I did the first 2 parts, i am really stuck on C, when i try to do (150/x) + 30T +(450/x) I get t=-60
Could somebody please point me in the right direction thanks :smile:
You should post the first two parts - the questions are interconnected and may use the previous answers

Well when solving you should always look for relationships. t1 and t2 has a relationship.

A/Deceleration = change in velocity/time

In both the acceleration and deceleration the change in velocity is the same so they are inversely proportional to each other. Three times the acceleration/deceleration three times less the time. So you can form an equation relating t2 to t1.

So now you have three variables to solve. X, t1 and T. Notice that there is a relationship with X and t1 too. V=u + at. So it boils down to two variables to be solved.

When you're solving for two variables you are looking for a simultaneous equations. Two variables so two of them.

The key pieces of data they have given is total time and total distance. So build two equations using these and quantities from the graph and solve them. Solve for T.

Then go for X.

Hope it helps your understanding.

Posted from TSR Mobile

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