Question

A particle initially located at the origin has an acceleration of vector a = 2.00ĵ m/s2 and an initial velocity of vector v i = 9.00î m/s.(a) find the vector position of the particle at any time t (where t is measured in seconds).

Answer 1

The position S(t) at any time of the particle can be written as
$S(t)=S_0 + vt + \frac{1}{2}at^2$
where $S_0$ is the initial position (in our case, the particle is initially located at the origin, so S0=0i+0j, v is the velocity, a the acceleration and t the time. 

Using v(t)=9.00 i m/s and a(t)=2.00 j m/s^2, we can rewrite S(t), the vector position of the particle at time t:
$S(t)=9t \mbox{\bf{i}} m/s + \frac{1}{2} 2 t^2 \mbox{\bf{j}} m/s^2$