- #1

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## Homework Statement

Acceleration is defined as the second derivative of position with respect to time: a = d

^{2}x/dt

^{2}. Integrate this equation with respect to time to show that position can be expressed as x(t) = 0.5at

^{2}+v

_{0}t+x

_{0}, where v

_{0}and x

_{0}are the initial position and velocity (i.e., the position and velocity at t=0).

## Homework Equations

a = d

^{2}x/dt

^{2}

x(t) = 0.5at

^{2}+v

_{0}t+x

_{0}

## The Attempt at a Solution

Hi everyone, thank you for the help. I am struggling with this one as I don't exactly know how to start. After doing some research online, it seems that

d

^{2}x/dt

^{2}is equal to vdv/dx, which can help towards solving the problem, but I don't understand why these are equal, or what was done to get there. Thank you for the help.