Police car and speeder when do they meet?

[endeavor]

Homework Statement
An unmarked police car traveling a constant 95km/h is passed by a speeder traveling 140 km/h. Precisely 1.00s after the speeder passes, the policeman steps on the accelerator; if the police car's acceleration is 2.00m/s², how much time passes before the police car overtakes the speeder (assumed moving at constant speed)?

v_0p = 95 km/h = 26.389 m/s
v_0s = 140 km/h = 38.889 m/s
a_p = 2.00 m/s
t₁ = 1.00 s
v_s = v_0s

Homework Equations

x = x₀ + v₀t + 0.5 * a * t²

The Attempt at a Solution

Let t₂ = the time it takes them to meet after the initial 1.00s.
After 1.00s, the x_p = 26.389m and x_s = 38.889m. Taking these two quantities as our initial positions, x_0p and x_0s, we have:
x_p = x_0p + v_0pt₂ + 0.5 * a_p * t₂²
x_s = x_0s + v_0st₂
Setting these two equal, I get a quadratic equation and find t₂ = 13.43 s or -0.9307 s. The total time would then be 14.43s...

But wait. Shouldn't the negative answer for t₂ be -1.00s?? Because 1.00s in the past, the cars met... So I must be doing something wrong...

 

[Hootenanny]

But wait. Shouldn't the negative answer for t₂ be -1.00s?? Because 1.00s in the past, the cars met... So I must be doing something wrong...

Firstly, nice presentation Secondly, don't forget from 0.00s to 1.00s the police car wasn't accelerating, so the symmetry is slightly misleading.

 

[endeavor]

Firstly, nice presentation Secondly, don't forget from 0.00s to 1.00s the police car wasn't accelerating, so the symmetry is slightly misleading.

What do you mean "the symmetry is slightly misleading"?

Is my answer correct or wrong?

 

[Hootenanny]

Your method looks correct, but I ain't checking the math for you. The symmetry is misleading because t = -0.9307 would have been the time they would have met if the police car would have been accelerating from t = 0.

Does that make sense?

 

[endeavor]

Your method looks correct, but I ain't checking the math for you. The symmetry is misleading because t = -0.9307 would have been the time they would have met if the police car would have been accelerating from t = 0.

Does that make sense?

Oh I see...
I forgot about that.

thanks

 

[Hootenanny]

Pleasure, once again great presentation.

 

[su zikai]

i cannt understand it

 

[WatermelonPig]

The position of the police officier is a piece-wise function.