You are arguing over a cell phone while trailing an unmarked police car by 25.0 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 6.00 m/s2. (a) What is the separation between the two cars when your attention finally returns? Suppose that you take another 0.400 s to realize your danger and begin braking. (b) If you too brake at 6.00 m/s2, what is your speed (in km/h) when you hit the police car?
To solve this problem, we need to break it down into steps and calculate the necessary values.
First, let's convert the speed from km/h to m/s. We know that 1 km/h is equal to 1000 m/3600 s, so we can convert the speed of 120 km/h to m/s:
Speed = 120 km/h * (1000 m/3600 s) = 33.33 m/s
Now, let's calculate the distance traveled by both cars during the 2.0 seconds when your attention is diverted. We can use the formula:
Distance = Initial velocity * time + 0.5 * acceleration * time^2
For the police car:
Initial velocity = 33.33 m/s
Acceleration = -6.00 m/s^2 (negative because it's braking)
Time = 2.0 s
Distance (police car) = 33.33 m/s * 2.0 s + 0.5 * (-6.00 m/s^2) * (2.0 s)^2
Distance (police car) = 66.66 m - 12.00 m
Distance (police car) = 54.66 m
For your car:
Initial velocity = 33.33 m/s
Acceleration = 0 m/s^2 (since you didn't start braking yet)
Time = 2.0 s
Distance (your car) = 33.33 m/s * 2.0 s + 0.5 * 0 m/s^2 * (2.0 s)^2
Distance (your car) = 66.66 m
The separation between the two cars when your attention returns is the difference between the distances traveled by each car:
Separation = Distance (police car) - Distance (your car)
Separation = 54.66 m - 66.66 m = -12.00 m
(a) The separation between the two cars when your attention finally returns is -12.00 meters. A negative value means that your car is behind the police car.
Now, let's calculate the speed of your car when it hits the police car. We can use the formula:
Final velocity = Initial velocity + acceleration * time
For your car:
Initial velocity = 33.33 m/s
Acceleration = -6.00 m/s^2 (since you're braking)
Time = 0.400 s
Final velocity (your car) = 33.33 m/s + (-6.00 m/s^2) * 0.400 s
Final velocity (your car) = 33.33 m/s - 2.40 m/s
Final velocity (your car) = 30.93 m/s
Finally, let's convert the final velocity back to km/h:
Final velocity (your car) = 30.93 m/s * (3600 s/1000 m)
Final velocity (your car) = 111.35 km/h
(b) The speed of your car when it hits the police car is approximately 111.35 km/h.
It's important to note that this solution assumes constant acceleration and neglects factors such as reaction time and the possibility of the police car decelerating further.
Vo = 120km/h = 120000m/3600s=33.33 m/s.
d1 = Vo*t + 0.5a*t^2
d1 = 33.33*2 + (-3)*2^2 = 54.66 m Traveled by policeman in 2 s.
d2 = Vo * t = 33.33 * 2 = 66.66 m/s. =
Distance traveled by me in 2 s.
d3 = Do - (d2-d1)
d3=25 - (66.66-54.66)=13 m = Separation
between me and the policeman.
b. d1 = Vo * t = 33.33 * 0.40 = 13.33 m
Oops! I hit the cop.
Speed = 120 km/h Because I hit the car before I started breaking.