Motion problem for constant acceleration of truck

[chroncile]

Homework Statement

A truck travels at a constant speed of 28.0 m/s in the fast lane of a two-lane highway. It approaches a stationary car stopped a the side of the road. When the truck is still 125 m behind the car, the car pulls out into the slow lane with an acceleration of 2.6 m/s2. How long will it take the truck to reach the car? (Answer is 6.32 s)

Homework Equations

d_t = d_c + 125
d_c = 1.3t²

The Attempt at a Solution

Okay I got the answer, but it's in quadratic form so:

1.3t² - 28.0t + 125 =

t = 15.2 s or t = 6.32 s

How do you know which answer is the correct one?

 

[chroncile]

Hello? Please, I need help

 

[zgozvrm]

How did you come up with your equation? You must have started from the basic kinematic equations, right?

Go back to those and try both values of t to see which one works/makes more sense.

 

[zgozvrm]

Think about what this means...

At the end of t=6.32s, how fast is each vehicle moving (what are their velocities)?
What is the distance covered by each in this time interval?

What about at t=15.2s?

 

[chroncile]

Yes, I asked the teacher and he explained it to me, but can you please answer my other question:

https://www.physicsforums.com/showthread.php?p=2893931#post2893931