SOLUTION: a body at rest attains a velocity V after free falling through distance h. Calculate the further distance the body is to travel to attain velocity 2V.

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Question 885741: a body at rest attains a velocity V after free falling through distance h. Calculate the further distance the body is to travel to attain velocity 2V.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You can learn physics, write/juggle formulas, and/or apply calculus, but the answer is simple and easy once you find it.
When starting from rest, and under constant acceleration,
final velocity is proportional to time, t ,
and distance is proportional to time squared t%5E2 .
To double the velocity requires to double the time, and that quadruples the total distance traveled.
To speed up to double the velocity, 2V , it will take 2t.
As time increases by a factor of 2 ,
distance (proportional to t%5E2 ) increases by a factor of 2%5E2=4 .
While going from 0 to 2V, the distance traveled is 4h ,
so the body travels 4h-h=highlight%283h%29 further.

JUGGLING FORMULAS:
Starting from rest, and at a constant acceleration, g ,
the velocity after a time t will be V=gt ,
and the distance traveled will be t times the average velocity %280%2BV%29%2F2=V%2F2 .
So, h=%28V%2F2%29%2At=V%2At%2F2=gt%2At%2F2=gt%5E2%2F2=%28g%2F2%29t%5E2 .
Also, since V=gt<--->t=V%2Fg ,
h=%28V%2F2%29%2At=%28V%2F2%29%2AV%2Fg-->h=V%5E2%2F2g gives you the relation of final velocity attained to total distance traveled.
If final velocity is 2V and the additional distance is x,
the total distance is
h%2Bx=%282V%5E2%29%2F2g--->h%2Bx=4V%5E2%2F2g--->h%2Bx=4%28V%5E2%2F2g%29--->h%2Bx=4h--->x=4h-h--->x=highlight%283h%29 .