document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #603470 by Fombitz(32388) $\"\"$ $\"About$

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Velocity is the derivative of distance with respect to time.
\n" ); document.write( " $\"s=k%2Asqrt%28t%29\"$
\n" ); document.write( " $\"v=ds%2Fdt=k%2A%281%2F2%29t%5E%28-1%2F2%29\"$
\n" ); document.write( "Acceleration is the derivative of velocity with respect to time.
\n" ); document.write( " $\"a=dv%2Fdt=-%28k%2F4%29%2At%5E%28-3%2F2%29\"$
\n" ); document.write( "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.
\n" ); document.write( "Acceleration varies as the cube of the velocity.
\n" ); document.write( " \n" ); document.write( "

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