Cars, Energy, and Work

[Soaring Crane]

If it takes 50 m to stop a car initially moving at 25 m/s, what distance is required to stop a car moving at 50 m/s under the same condition?

a. 50 m
b. 100 m
c. 200 m
d. 400 m

This is probably a really easy question, but I just can't see how to work it out. I tried to set up a ratio between the distance and velocity and that got me 100 m, but b is incorrect. Can anyone explain the correct method to do this problem and tell me why setting up a ratio between those 2 components is a mistake?

[UrbanXrisis]

Answer is C

Vf^2=Vi^2+2ad
0=25^2+2(a)50
a=-6.25m/s^2

now you know the deceleration of the car

Vf^2=Vi^2+2ad
0=50^2+2(6.25)d
d=200m

[Soaring Crane]

Thanks. Is this the only way you can solve it?

[UrbanXrisis]

This is the way I would solve it. Hope others give some posts