Integration of Velocity function to Position Function?

[engineertobe]

I was given the acceleration function and had to integrate to get the velocity function, I know that the answer I got was right. Now I must integrate the velocity function to get the position function.

The answer should be x(t)=x0+(v0/k)(1-e^-kt).

The velocity equation is v(t)=v0(e^-kt).

I keep getting x=(v0/-k)(e^-kt)+C. Where am I going wrong?

 

[tkhunny]

Why do you think you are going wrong?

\(\displaystyle x_{0} + \frac{v_{0}}{k}(1-e^{-kt}) = x_{0} + \frac{v_{0}}{k} - \frac{v_{0}}{k} e^{-kt} = \frac{v_{0}}{-k} (e^{-kt}) + C\)

It's all in the constant.