Two cars pass each other traveling at the same speed. one car has a constant velocity of 15.0 m/s, east. the other car has a constant acceleration of 1.00 m/s, west. how much time will have elapsed until the cars are 164 m apart?

The formula for calculating the distance at constant velocity is:

d = v * t

d = 15 t

The formula for distance at constant acceleration is:

d = v0 t + 0.5 a t^2

d = 15 t + 0.5 t^2

So after a sum distance of 164 m:

15 t + (15 t + 0.5 t^2) = 164

30 t + 0.5 t^2 = 164

t^2 + 60 t = 328

(t + 30) ^2 = 328 + 30^2

t + 30 = ± 35.04

t = - 65.04, 5.04

Since time cannot be negative, so the two cars are 164 m apart after about 5 seconds