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M1 position vector question

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1. hi, please can anyone help me with part b? I have got up to the 5t^2-30t+50 part but I have no idea what d^2 is. The mark scheme shows completing the square and I don't understand what is 5 and why t is somehow 3... Thanks! Please try to explain it simply.
2. (Original post by coconut64)
hi, please can anyone help me with part b? I have got up to the 5t^2-30t+50 part but I have no idea what d^2 is. The mark scheme shows completing the square and I don't understand what is 5 and why t is somehow 3... Thanks! Please try to explain it simply.
We talked about this before, remember? It's a maximisation/minimisation problem. You have d^2 as a quadratic and you want to find the minimum point of d^2. There are two ways of finding the minimum point of a quadratic, either by differentiation or by completing the square.

Anyhow, you have . Do you still remember how to complete the square?

You have so you do but that gets you so you need to add one.

Hence you have .

Hence, you have:

Now, if you remember your C2/C1/Whatever, you should remember that this means your minimum point is at - if you don't, then I strongly recommend you go look up completing the square in your textbook.

So the minimum value of occurs when and the minimum value is .

That's a bit like me saying has a minimum at - i.e: the minimum occurs when and the minimum value is . Except, in this case, is your and is your .
3. (Original post by Zacken)
We talked about this before, remember? It's a maximisation/minimisation problem. You have d^2 as a quadratic and you want to find the minimum point of d^2. There are two ways of finding the minimum point of a quadratic, either by differentiation or by completing the square.

Anyhow, you have . Do you still remember how to complete the square?

You have so you do but that gets you so you need to add one.

Hence you have .

Hence, you have:

Now, if you remember your C2/C1/Whatever, you should remember that this means your minimum point is at - if you don't, then I strongly recommend you go look up completing the square in your textbook.

So the minimum value of occurs when and the minimum value is .

That's a bit like me saying has a minimum at - i.e: the minimum occurs when and the minimum value is . Except, in this case, is your and is your .
Oh yeah, I can never relate the two together, it never occurred to me that it is about minimum points! Anyway cheers again.
4. (Original post by Zacken)
We talked about this before, remember? It's a maximisation/minimisation problem. You have d^2 as a quadratic and you want to find the minimum point of d^2. There are two ways of finding the minimum point of a quadratic, either by differentiation or by completing the square.

Anyhow, you have . Do you still remember how to complete the square?

You have so you do but that gets you so you need to add one.

Hence you have .

Hence, you have:

Now, if you remember your C2/C1/Whatever, you should remember that this means your minimum point is at - if you don't, then I strongly recommend you go look up completing the square in your textbook.

So the minimum value of occurs when and the minimum value is .

That's a bit like me saying has a minimum at - i.e: the minimum occurs when and the minimum value is . Except, in this case, is your and is your .

Oh yeah, I can never relate the two together, it never occurred to me that it is about minimum points! Anyway cheers again.
5. (Original post by coconut64)
Oh yeah, I can never relate the two together, it never occurred to me that it is about minimum points! Anyway cheers again.
No worries.

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