Acceleration is defined as the second derivative of position with respect to time: a = d2x/dt2. Integrate this equation with respect to time to show that position can be expressed as x(t) = 0.5at2+v0t+x0, where v0 and x0 are the initial position and velocity (i.e., the position and velocity at t=0).
a = d2x/dt2
x(t) = 0.5at2+v0t+x0
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
d2x/dt2 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.