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.

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) (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, ,
and distance is proportional to time squared .
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 ,
distance (proportional to ) increases by a factor of .
While going from 0 to 2V, the distance traveled is ,
so the body travels further.

JUGGLING FORMULAS:
Starting from rest, and at a constant acceleration, ,
the velocity after a time will be ,
and the distance traveled will be times the average velocity .
So, .
Also, since <---> ,
--> gives you the relation of final velocity attained to total distance traveled.
If final velocity is and the additional distance is ,
the total distance is
--->--->--->--->---> .
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