# Police car and speeder when do they meet?

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)?

v0p = 95 km/h = 26.389 m/s
v0s = 140 km/h = 38.889 m/s
ap = 2.00 m/s
t1 = 1.00 s
vs = v0s

2. Homework Equations
x = x0 + v0t + 0.5 * a * t2

3. The Attempt at a Solution
Let t2 = the time it takes them to meet after the initial 1.00s.
After 1.00s, the xp = 26.389m and xs = 38.889m. Taking these two quantities as our initial positions, x0p and x0s, we have:
xp = x0p + v0pt2 + 0.5 * ap * t22
xs = x0s + v0st2
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...

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Hootenanny
Staff Emeritus
Gold Member
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.

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
Staff Emeritus
Gold Member
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?

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...

thanks

Hootenanny
Staff Emeritus