When calculating the postition, velocity, and acceleration of an object?

Question

isn't it possible to calculate a negative time value if you are not given time is greater than or equal to zero?

Answer 1

No. You must remember that a negative sign in physics is basically a directional sign - not the same use as in math.

Answer 2

When you pick a certain time to be zero in a problem, it's an arbitrary point. So, if you calculate a value for t < 0, it only means it happened before the zero point you arbitrarily picked.
This can happen when you solve a quadratic in t like the distance function for constant acceleration: d = Vt + ½at²