Question

Find v(T) and the position equation given that a(T)=12t+3, v(2)=9, and s(1)=-2.

Answer 1

a(t) = v'(t)

so if a(t) = 12t+3
v(t) = 6t^2 + 3t + c
given: v(2) = 9 ---> 9 = 6(2)^2 + 3(2) + c
c = -21
so v(t) = 6t^2 + 3t - 21

s(t) = 2t^3 + (3/2)t^2 - 21t + k
given: s(1) = -2 ----> -2 = 2(1) + 3/2 - 21 + k
k = 31/2

s(t) = 2t^3 + (3/2)t^2 - 21t + 31/2