You are arguing over a cell phone while trailing an unmarked police car by 25 m; both your car and the police car are traveling at 110 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 5.0 m/s^2. If you too brake at 5.0 m/s^2, what is your speed when you hit the police car?
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Nice. For both cars, you want to write down an equation for the position of each car at time t.
At time t = 0, let us say that position of police car, write s_p, s_p(t=0) = 25
At time t = 0, that means the position of your car, write s, s(t=0) = 0
s_p(0) = 25
s(0) = 0
Now both cars are traveling at an initial speed of 110 km/hr. That is u = 30.6 m/s
If neither cars decelerated, their equations of motion would be
s_p(t) = 25 + 30.6t
s(t) = 30.6t
Now you figure out how to incorporate the deceleration. The two cars collide when
s_p(t) = s(t)