SOLUTION: If the distance traveled varies as the square root of the time, prove that the acceleration varies as the cube of the velocity.

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Question 982608: If the distance traveled varies as the square root of the time, prove that the acceleration varies as the cube of the velocity.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Velocity is the derivative of distance with respect to time.
s=k%2Asqrt%28t%29
v=ds%2Fdt=k%2A%281%2F2%29t%5E%28-1%2F2%29
Acceleration is the derivative of velocity with respect to time.
a=dv%2Fdt=-%28k%2F4%29%2At%5E%28-3%2F2%29
So then velocity is inversely proportional to the square root of time and acceleration is inversely proportional to the cube of the square root of time.
Acceleration varies as the cube of the velocity.