Question Part Points Submissions Used You are arguing over a cell phone while tr

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Question Part
Points
Submissions Used
You are arguing over a cell phone while trailing an unmarked police car by 32 m. Both your car and the police car are traveling at 100 km/h. Your argument diverts your attention from the police car for 1.5 s (long enough for you to look at the phone and yell, "I won't do that!"). At the beginning of that 1.5 s, the police officer begins emergency braking at 5 m/s2.
(a) What is the separation between the two cars when your attention finally returns?

My answer: 26.375s (correct)

(b) Suppose that you take another 0.4 s to realize your danger and begin braking. If you too brake at 5 m/s2, what is your speed when you hit the police car?

I've tried 34.2, 51.89,and 18 km/h (all incorrect)

Explanation / Answer

Formula to find my distance travelled [latex]Dist = Speed x Time = 30.55 m/s x 1.9 = 58.045 m[/latex] Distance travelled by cop car de-accelerating [latex]D(t) = -2.5t^2+30.55t = -2.5(1.9^2)+30.55(1.9) = 49.02[/latex] To find new distance of separation, adding the distance travel when cop begins to brake to 37, equates to 86.02 subtracting my distance from this distance equates to 86.02 - 58.045 = 27.975 Now after this time duration I begin to de-accelerate as well, I first find the velocity of the cop at the end of this time period, here, equates to [latex]v(t) = -5(1.9)+30.55 = 21.05 [/latex] Making a new equations for both car's positions and new equation for cop's velocity so I can find the time which they impact or "intersect" I arrive to Cop's New Velocity Formula [latex] -5(t)+21.05[/latex] Cop's Position Formula [latex]-2.5(t^2)+21.05(t)+27.975[/latex] My Car's Velocity Formula [latex]-5(t) + 30.55[/latex] My Car's Position Formula [latex]-2.5(t^2)+30.55(t)[/latex] Now setting these two new position formulas/functions to each other and solving for t, and plugging the time into my car's velocity formula and converting the units over back to km/h I will arrive at a possible solution Solving for time, t. [latex]-2.5(t^2)+30.55(t) = -2.5(t^2)+21.05(t)+27.975[/latex] [latex]30.55(t)-21.05(t) = 27.975[/latex] [latex]9.5t=27.975[/latex] [latex]t = 2.9394 s[/latex] Plugging this into the formula for my velocity [latex]-5(2.9394)+30.55 = 15.853 m/s[/latex] Converting this back to km / h equates to 57.0708 km/h

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