A particle is moving with acceleration a(t)=2-3t, t=0: v(0)=-1 and s(0)=1. Determine s(2)

Question

A particle is moving with acceleration a(t)=2-3t, t=0: v(0)=-1 and s(0)=1. Determine s(2)

Answer 1

a(t) = 2-3t

v(t) = 2t -3t^2/2 + C

v(0) =-1= C

v(t) = 2t -3t^2/2 -1

s(t) = integral of v(t) =t^2 -t^3/2 -t+ C2

s(0) = 1 = C2

s(2) = 2^2 -(2^3)/2 - 2 + 1

= 4-4-2+1

= -1