Distance when velocity doubles

[KEVIN Phlem]

Homework Statement

A certain airport runway of length L allows planes to accelerate
uniformly from rest to takeoff speed using the full length of
the runway. Because of newly designed planes, the takeoff
speed must be doubled, again using the full length of the runway
and having the same acceleration as before. In terms of L,
what must be the length of the new runway?

Homework Equations

Not sure how to evens start.

The Attempt at a Solution

in my head i said that the runway would double buy i was wrong.

 

[jbriggs444]

If you need double the speed and you have the same acceleration, by what factor must you increase the time interval? That's an easier problem. Can you find a relevant equation?

Using that answer, what can you conclude about the distance required?