A Level Mechanics.

In this question, the vectors i and j and unit vectors east and north respectively.
(a) A particle moves in two dimensions with constant acceleration. Initially it has
position vector 3i+2j m relative to a fixed origin and has initial velocity i+j ms-1.
After 4 seconds it has position vector 7i-4j m.
What is its velocity at that time? [4]
(b) The particle then continues at constant speed.
Calculate how long the particle has been travelling at constant speed when it is southeast of the origin. [4]

I did part a using s=1/2(u+v)t

For part b, I know that SE i and j components will be equal. How do I start this question?

SE, the position vector will be
xi - xj
so the j coefficient is negative and you want to find the time when this occurs. You have the position vector and (constant) velocity vector at 4s, so just use hte usual speed-distance-time formula to solve (simultaneously) for the time.

SE, the position vector will be
xi - xj
so the j coefficient is negative and you want to find the time when this occurs. You have the position vector and (constant) velocity vector at 4s, so just use hte usual speed-distance-time formula to solve (simultaneously) for the time.

How would you solve it simultaneously?

Not sure what you think "it" is, it would be good to upload your thoughts. But you should set up a couple of equatoins to represent the motion in that phase and note that at a certain time, the position will be SE of the origin so the coordinate displacements are related. You could do a geometry or relative motion approach as well.

I have the constant velocity and position vector points at 4 seconds. Velocity = i - 4j and position vector = 7i - 4j and when using the speed distance time equation, you get time= distance/speed. But how does that help as the position and velocity are in component form...?

The
distance = speed*time
applies to both the i and j directions seperately to give two simultaneous equations. Or it could be applied in the direction of motion. Its just a very simple suvat
s = ut + 1/2 at^2
where a=0 so its really not different.

Okay so using the Suvat method, I am confused with what values you would substitute in. I keep ending up with t=7 or t=1 when subbing in the values of position and velocity that I already have?