Particle has position vector 2i + j

1. Feb 20, 2005

Gughanath

A particle has position vector 2i + j (i is along x axis and j is along y axis) initially. and is moving with speed of 10m/s in the direction 3i-4j. Find its position vector when t=3 and the distance it has travlled in those 3 seconds.
Please help me with the first part of the question.

2. Feb 20, 2005

arildno

Your velocity vector must satisfy two conditions:
1. It must be parallell to 3i-4j
What does that tell you about the form of the velocity vector?
2. The velocity vector's magnitude is 10.

3. Feb 20, 2005

Gughanath

it says the particle is travelling in the direction 3i-4j, isnt that the velocity vector??

4. Feb 20, 2005

arildno

Nope: the velocity vector is the time-derivative of the position vector.
What you've been given is that the velocity vector is PARALLELL to (in the direction of) 3i-4j, that is:
$$\vec{v}=k(3\vec{i}-4\vec{j})$$
where k>0 is a proportionality factor (unknown at the moment!).
In addition, you have been given that the SPEED is 10, that is:
$$||\vec{v}||=10$$
Use the last equation to determine k.

5. Feb 20, 2005

Gughanath

phew...you just saved me from a headache. Now I get it. My value for k is 2.

6. Feb 20, 2005

Gughanath

displacement is 20i -23j

7. Feb 21, 2005

arildno

Yes, that's right.