Question

Two cars are approaching one another in the same lane of a highway. One has a speed of 30m/s, the other a speed of 20m/s when they are 96m apart. The drivers simultaneously apply brakes to avert a collision. Both cars lose speed at 6.0m/s^2. How long after the application of brakes do the cars collide? Where are the cars and at what speeds are they travelling when they collide?

dA = v1t + 1/2 at^2
= 30t - 3t^2

dB = v1t + 1/2 t^2
= 20t - 3t^2

dA+dB = 96
30t - 3t^2 + 20t - 3t^2 = 96
50t - 6t^2 = 96
- 6t^2 + 50t - 96 = 0
*dividing both sides by -2*
3t^2 - 25t + 48
Should I factor with the quadratic formula?

And then I have no idea how to answer this question -
Where are the cars and at what speeds are they travelling when they collide?

Answer 1

You have it!
Solve the quadratic. You will get 2 answers. One of them, the lower, is the impact time. The other is a "phantom event" where again the distance 96m when the cars back up because the negative acceleration. That event, of course, does not happen.