Help w/ PHYSICS QUESTION! Two soccer players start from rest, 51 m apart...?

Question

Two soccer players start from rest, 51 m apart. They run directly toward each other, both players accelerating. The first player has an acceleration whose magnitude is 0.50 m/s2. The second player's acceleration has a magnitude of 0.38 m/s2.

How much time passes before they collide?

Answer 1

(df- di) (change in distance) = .5at^2 + (t)vo (initial velocity)

a1 = .50  vo= o

d= .5(.5)t^2 = .25t^2

a2 = .38 vo=0

df= .5(-.38)t^2 + 51 (This is di) = .19t^2+51

one acceleration must be negative compared to the other.

set them equal to each other.

.25t^2 = -.19t^2 + 51

.44t^2 = 51

t= 10.77 seconds

Answer 2

10.77 secs

use equation ut + 1/2at^2 = s