Question

Find s(t), where s(t) represents the position function and v(t) represents the velocity function. v(t) = 12:2, s(0) = 8 s(t)=

Answer 1

we have that

v(t)=12t^2

to obtain the position function, integrate the velocity function

so

`s(t)=\int 12t^2dt=4t^3+C`

REmember that

s(0)=8

so

For t=0 s(t)=8

substitute

8=4(0^3)+C

c=8

therefore

s(t)=4t^3+8