Physics: instantaneous velocity?

Question

A particle has a constant acceleration of a = (6i + 4j) m/s^2. At time t =0, the velocity is zero and the position vector is r - (10m) i. Find the velocity and position vectors at any time, t.

Answer 1

V = At where V and A are vectors. The velocity will be in the same direction as the acceleration. So:

V = (6ti + 4tj) m/s

The position vector depends on how far the particle has moved in the time t and this is given by:

S = V0t + (1/2)At^2
Now V0 = 0 since the particle starts from rest so:
S = (1/2)At^2
S = (3t^2i + 4t^2j) m

This must then be added to the starting position giving:

R = R0 + S
R = 10i + (3t^2i + 4t^2j) m
R = (10 + 3t^2)i + 4t^2j