Particle has position vector 2i + j

[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.

 

[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.

 

[Gughanath]

it says the particle is traveling in the direction 3i-4j, isn't that the velocity vector??

 

[arildno]

it says the particle is traveling in the direction 3i-4j, isn't that the velocity vector??

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.

 

[Gughanath]

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

 

[Gughanath]

displacement is 20i -23j

 

[arildno]

displacement is 20i -23j

Yes, that's right.