Integral Calculus Express v and s in terms of t

Question

A particle is moving along a line according to the equation of motion s = f(t) where s is in ft and t in seconds.

1) Given a = 2 t 2t − ; s = 1 when t = 0 and s = -3 when t = 2. Express v and s in terms of t.

Answer 1

This is a direct application of integration.

v (t) = ∫a(t) dt

and s(t) = ∫v(t) dt.

Use the initial conditions to determine the constants of integation.