urgent help, A Level Maths Mechanics

A particle has position vector 2i+jinitially and is moving with speed 10ms^-1 in the direction 3i- 4j. Find its position vector when t = 3.

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- Sep 26th 2008, 04:58 AMCarl FelthamPosition vectors
urgent help, A Level Maths Mechanics

A particle has position vector 2**i**+**j**initially and is moving with speed 10ms^-1 in the direction 3**i**- 4**j**. Find its position vector when t = 3. - Sep 26th 2008, 05:41 AMmr fantastic
- Sep 26th 2008, 05:58 AMCarl Felthami do not understand
Unit vector in direction of 3i - 4j is (3i - 4j)/5. Therefore v = 10 (3i - 4j)/5 = 6i - 8j.

Therefore dx/dt = 6i - 8j => x = 6ti - 8tj + C.

When t = 0, x = 2i + j therefore C = 2i + j.

Therefore x = (6t + 2) i + (1 - 8t) j.

I understand the rest, bar how you managed to come about the two statements highlighted in red. Why is the first divided by and, and the second doubled? - Sep 26th 2008, 06:08 AMmr fantastic
Remember that velocity is a vector and vectors have a magnitude and a direction. The direction of v is the unit vector in the direction of 3i - 4j. The magnitude of v is its speed 10 m/s. So you multiply the unit vector by 10 (the magnitude of the velocity) to get the velocity vector.

How to get a unit vector: Divide the given vector by its magnitude. The magnitude of 3i - 4j is 5. Therefore you divide 3i - 4j by 5 to get a unit vector in the direction of 3i - 4j.

10 (3i - 4j)/5 = 2 (3i - 4j) = 6i - 8j.