# Can someone explain this assumption to me for integration ?

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#1
In this markscheme :

I understand the workings but don't get where this assumption comes from. Could someone please explain ? Thanks.

Last edited by seals2001; 4 weeks ago
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4 weeks ago
#2
What's the question and mark scheme?
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4 weeks ago
#3
(Original post by seals2001)
In this markscheme :

I understand the workings but don't get where this assumption comes from. Could someone please explain ? Thanks.

You're aware of the difference between distance travelled and displacement?
If the velocity changes sign, they will be different. Velocity changing sign corresponds to having both positive and negative area between the velocity curve and the time axis. To get the total distance, you'd have to treat all areas as positive. Hence the assumption.
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4 weeks ago
#4
(Original post by mqb2766)
You're aware of the difference between distance travelled and displacement?
If the velocity changes sign, they will be different. Velocity changing sign corresponds to having both positive and negative area between the velocity curve and the time axis. To get the total distance, you'd have to treat all areas as positive. Hence the assumption.
Kind of weird that the solution makes it clear it's at least considering the distinction, but then doesn't consider that -50 = 44 + c would also give a valid solution.
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4 weeks ago
#5
(Original post by DFranklin)
Kind of weird that the solution makes it clear it's at least considering the distinction, but then doesn't consider that -50 = 44 + c would also give a valid solution.
Yeah, as you say, given that the acceleration is positive, a large enough negative initial velocity would still be negative in that time interval. They obviously wanted to rule out the case of a smaller, initial negative velocity so the velocity flips sign in that time interval. It would also have been good not to use "v" for the displacement as well as it may confuse with the use of "v" for velocity on the preceding (and following) line ... Obviously a bit of dynamic variable definition.
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