suppos the velocity is given by v=9t^4. Find the displacement as a function of time if s=6 when t=0
If velocity = v(t), then
displacement s(t) = ∫v(t)
Use s(0)=6 to determine the constant of integration.
For example, if
v(t)=3x² then
s(t)=∫v(t)=x³+C
Given s(1)=4, we have
1³+C=4 => C=3
So
s(t)=x³+3