Question

You are arguing over a cell phone while trailing an unmarked police car by 26.0 m; both your car and the police car are traveling at 120 km/h. Your argument diverts your attention from the police car for 2.0 s (long enough for you to look at the phone and yell,“I won't do that!”). At the beginning of that 2.0 s, the police officer begins braking suddenly at 5.20 m/s^2. (a) What is the separation between the two cars when your attention finally returns? Suppose that you take another 0.500 s to realize your danger and begin braking. (b) If you too brake at 5.20 m/s^2, what is your speed when you hit the police car?

Answer 1

Question

You are arguing over a cell phone while trailing an unmarked police car by $26.0 \, \text{m}$; both your car and the police car are traveling at $120 \, \text{km/h}$. Your argument diverts your attention from the police car for 2.0 s (long enough for you to look at the phone and yell, "I won't do that!"). At the beginning of that 2.0 s, the police officer begins braking suddenly at $5.20 \, \text{m/s}^2$. (a) What is the separation between the two cars when your attention finally returns? Suppose that you take another 0.500 s to realize your danger and begin braking. (b) If you too brake at $5.20 \, \text{m/s}^2$, what is your speed when you hit the police car?

Solution

a) $l = 26 \, \text{m}; \quad v_{01} = v_{02} = v = 120 \, \text{km/h} \approx 33.333 \, \text{m/s}; \quad t = 2 \, \text{s}, \quad a_1 = 0; \quad a_2 = a = 5.2 \, \text{m/s}^2$.

Our car: $x_{1} = v_{01}t = vt$.

Police car: $x_{2} = l - v_{02}t + a_{2}t^{2}/2 = l - vt + at^{2}/2$.

The separation between the two cars: $\Delta x = x_{2} - x_{1} = l - 2vt + at^{2}/2 = -96.932 \, \text{m}$.

It means that cars hit before end of 2 s. Answer: $\Delta x = 0$.

b) The speed of our car is $33.333 \, \text{m/s}$, because we can't return our attention (cars hit before end of 2 s). Answer: $v = v_{01} = 120 \, \text{km/h} \approx 33.333 \, \text{m/s}$.

P.S. I guess condition of the problem contain mistake. I think initial separation between the two cars is bigger. Please check it and if you want write me back, I'll do it again.

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