Is My Approach to Solving the Particle Motion Problem Correct?

[BeckyStar678]

am i doing this problem right? help please!

Homework Statement

a particle initially located at the origin has an acceleration of a=3 j m/s2 and an initial velocity of vi= 5 i m/s. find a.) the vector position and velocity of the particle at any time t and b.) the coordinates and speed of the particle at t=2 s.

Homework Equations

The Attempt at a Solution

so for a.) i got the equation xf=0+5(t)+.5(3)(t²) I am not really sure where to go from there. it says for any time, so do i just put in any number
to get the velocity i did vf=5+3(t)

for b.) do i just plug in 2 for the times above. I am really not sure if I am doing this right

 

[danago]

Homework Statement

a particle initially located at the origin has an acceleration of a=3 j m/s2 and an initial velocity of vi= 5 i m/s. find a.) the vector position and velocity of the particle at any time t and b.) the coordinates and speed of the particle at t=2 s.

Homework Equations

The Attempt at a Solution

so for a.) i got the equation xf=0+5(t)+.5(3)(t²) I am not really sure where to go from there. it says for any time, so do i just put in any number
to get the velocity i did vf=5+3(t)

for b.) do i just plug in 2 for the times above. I am really not sure if I am doing this right

When it says at any time, i think its just saying come up with an equation that gives the displacement for any given value of t, so you would leave t as a variable.

And yea then just plug t=2 into the equations

EDIT: Besides what i missed about the vectors, and tony mentioned below :)

 

[tony873004]

Your answer should have $${\rm{\hat i}}$$ and $${\rm{\hat j}}$$ in them, or your answer is not in vector notation.