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# quick help with a M1 intergration question watch

1. I cannot find out to find out what C is when you intergrate.
In this following question during the intergration part of getting displacement how do i find out what c equals?
here the question:
A particle moves in a straight line. Its velocity at time t s is v ms-1, where v= 0.3t^2 + 4t
Find:
(i) find an expression for the acceleration of the particle in terms of t.
The particle passes through the point A with velocity 20.8ms-1
(ii) Find the displacement of the particle from A when its acceleration is 7ms-2
I can nearly do all of this question its just the bit in the middle where I dont understand how to find what C equals.
thanks
btw final answer to this question is 24.1metres

sorry i copied the question out wrong, just updated it
2. You need to know some conditions in order to find c. Did the particle start from rest, if so then v=0 at t=0.
3. sorry i copied the question out wrong
ive updated it now
4. You just need to call the point where it starts x=0. Since x=0 at t=0, then c=0
5. (Original post by Bezza)
You just need to call the point where it starts x=0. Since x=0 at t=0, then c=0
hmm ok...when it the point where X=O, at point A it has already been moving for awhile hasnt it?
6. (Original post by hero)
hmm ok...when it the point where X=O, at point A it has already been moving for awhile hasnt it?
Yeah, but because the question asks you about the displacement from the point A it's easiest just to call A the origin so at A, x=0, then x will be the displacement from A.
7. Calculate the value of t at the point A where the velocity is 20.8. you can't just say that it started at v=0 cos you dont know that.
8. (Original post by queen-of-pain)
Calculate the value of t at the point A where the velocity is 20.8. you can't just say that it started at v=0 cos you dont know that.
I said let x=0 initially, and having read the question I've realised it doesn't start at A crap. sorry! You do know that v=0 initially cos it gives you the eqn for v as a function of t.

You just find how far A is from the start point, and how far it is from the start point when a = 7 m/s^2, then subtract one from the other to calculate displacement from A.
9. s = 0.1t³ + 2t² + c
v= 0.3t² + 4t
a = dv/dt = 0.6t + 4

at A, v=20.8 m/s
=> t = 4 secs
=========
(using v= 0.3t² + 4t)

when a = 7m/s²
t = 5 secs
======
(using a = 0.6t + 4)

dist travelled is,

s(t=5) minus s(t=4)
= 0.1(5)³ + 2(5)² + c - 0.1(4)³ - 2(4)² - c
= 12.5 + 50 - 6.4 - 32
= 24.1
====
10. Ic thank you

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Updated: June 15, 2004
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