Question

A particle is moving with the given data. Find the position of the particle. a(t) = t-2, s(0) = 1, v(0) = 3

Answer 1

Your question should have defined:
a(t)=acceleration function of particle,
v(t)=velocity function
s(t)=position function.
Unless it is a physics problem (and not math).

Integrate a(t) w.r.t. t and use v(0)=3 to find the integration constant for v(t).
Integrate v(t) w.r.t. t and use s(0)=1 to find the integration constant for s(t).
s(t) is the position function.

Answer 2

It's a calculus problem. What formula should I use?

Answer 3

Have you done integration?

Answer 4

Did the problem define those terms?

Answer 5

@laurabird9

Answer 6

Question should have indicated that:
ds(t)/dt=v(t)
dv(t)/dt=a(t)
Since you are given a(t), you can find v(t) and eventually s(t) by successively integrating a(t) and v(t). Do not omit to use given values to find the integration constants.
Read the second part of my first answer.