Aparticle 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).

The position S(t) at any time of the particle can be written as

where  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: