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# M3 Integration Question

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1. EDIT TO QUESTION:

So, I work through part a) using the formula a = d/dx(1/2 v2) which gives me v = 2x1/2(x+3)1/2, which is wrong.

The answer is v = 2x + 3.

Not sure how to get there :/
2. (Original post by Alexion)
...
Do you understand why you're wrong for the first part?

For the second: velocity is the rate of change of displacement, so write and then it's a simple differential equation.

For your last question, when the question says that, all it is doing is introducing the variable as displacement/distance, as time and as velocity.
3. (Original post by Zacken)
Do you understand why you're wrong for the first part?
Not really, I keep getting the same thing as before :/

For the second: velocity is the rate of change of displacement, so write and then it's a simple differential equation.
It's easier now I know that the answer to the first bit's simpler, so that's alright now

For your last question, when the question says that, all it is doing is introducing the variable as displacement/distance, as time and as velocity.
Yep, that seems obvious now
4. (Original post by Alexion)
Not really, I keep getting the same thing as before :/
You know that acceleration is the rate of change of velocity so you can write then we have that . But that's in terms of so we need to use a little trick:

since they 'cancel' out. But is just the rate of change of displacement with time. That's velocity.

So indeed, we can write .

We now have a simple DE: .

5. (Original post by Zacken)
We now have a simple DE: .

But how do you get from v(dv/dx) = 4x + 6 to something that's just v = f(x)?
6. (Original post by Alexion)
But how do you get from v(dv/dx) = 4x + 6 to something that's just v = f(x)?
Separating the variables?
7. (Original post by Alexion)
But how do you get from v(dv/dx) = 4x + 6 to something that's just v = f(x)?
Uhm, well , you know that so , if that's the part you were confused with.

Otherwise:
8. (Original post by Zacken)
Uhm, well , you know that so , if that's the part you were confused with.

Otherwise:
OK NOW I SEE WHERE I WENT WRONG

I subbed in x = 0, v = 0 hence the problems with the resulting equation

Thanks for the help anyway
9. (Original post by Alexion)
...
No problem.

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