You are in a car that is traveling along a highway at a constant speed of 16 m/s. Suddenly you see a truck also traveling at a constant speed (3.0 m/s) that is on a track to cross your lane from an alley on the right and is moving into your lane (which you can't get out of, because of broader safety concerns like head on traffic in the other lane). Your car's maximum acceleration is 6.0 m/s^2 (either way, getting faster or slower) and your reaction time of 0.75 s between seeing the truck and applying the brake or the accelerator. The distance from the side street, where you first notice the truck, to the right edge of your lane is 2.0 m and the lane also has a fixed width of 4.0 m, check for yourself that all of these numbers are reasonable. You will assume a reasonable size for your car. The truck is 3.0 m wide.

a) How long will it take the truck from the moment you notice it, to block enough of your land so you can't slip past while also staying in your own lane (in seconds)?
b) How far will your car travel (in meters) while your brain is figuring out what to do?
c) If you decide that braking is in your best interests how long will it take you to come to a complete stop once you begin the process of braking (in s)?
d) What is the minimum distance (in m) you must be from the truck to successfully stop before hitting it?

a) Well, if the truck is moving at a constant speed of 3.0 m/s and it takes you some time to react, let's calculate how long it will take for the truck to block your lane. Remember that you have a reaction time of 0.75 s.

The distance from the side street to the right edge of your lane is 2.0 m, plus the width of your lane which is 4.0 m, plus the width of the truck which is another 3.0 m. So, the total distance the truck needs to travel to block your lane is 2.0 m + 4.0 m + 3.0 m = 9.0 m.

Since the truck is moving at a constant speed of 3.0 m/s, it will take the truck 9.0 m / 3.0 m/s = 3.0 s to block your lane.

b) During your reaction time of 0.75 s, your car will continue moving at a constant speed of 16 m/s. To calculate the distance your car will travel, we can use the formula d = v * t, where d is the distance, v is the velocity, and t is the time.

So, during your reaction time, your car will travel a distance of 16 m/s * 0.75 s = 12.0 m.

c) Let's assume you decide to brake to come to a complete stop. Your car's maximum acceleration is 6.0 m/s^2. To calculate how long it will take you to come to a stop, we can use the formula t = (vf - vi) / a, where t is the time, vf is the final velocity (0 m/s in this case since you want to stop), vi is the initial velocity (16 m/s), and a is the acceleration.

Using this formula, we can calculate the time it will take to come to a stop: t = (0 m/s - 16 m/s) / (-6.0 m/s^2) ≈ 2.67 s.

d) To calculate the minimum distance you must be from the truck to successfully stop before hitting it, we need to consider the distance it would take for your car to come to a complete stop.

Using the formula d = vi * t + (1/2) * a * t^2, where d is the distance, vi is the initial velocity (16 m/s), t is the time it takes to come to a stop (2.67 s), and a is the acceleration (-6.0 m/s^2), we can calculate the distance: d = 16 m/s * 2.67 s + (1/2) * -6.0 m/s^2 * (2.67 s)^2 ≈ 21.33 m.

Therefore, the minimum distance you must be from the truck to successfully stop before hitting it is approximately 21.33 meters.

To answer these questions, we need to break down the problem into different stages and calculate the relevant distances and times.

a) How long will it take the truck from the moment you notice it to block enough of your lane (in seconds)?

First, we need to calculate the time it takes for the truck to completely block your lane. Since the truck is moving perpendicular to your lane, we can consider it as an example of relative motion.

The width of the truck is 3.0 meters, and the width of your lane is 4.0 meters. This means that the truck needs to move a total distance of (3.0 + 4.0) = 7.0 meters to block your lane completely.

The relative velocity between the truck and your car is the difference between their speeds. In this case, it is (16 m/s - 3.0 m/s) = 13 m/s.

We can now use the formula: time = distance / velocity to calculate the time it takes for the truck to block your lane.

time = 7.0 meters / 13 m/s = 0.538 seconds

Therefore, it will take approximately 0.538 seconds for the truck to block enough of your lane, so you can't slip past while staying in your own lane.

b) How far will your car travel while your brain is figuring out what to do?

We need to calculate the distance your car will cover during the reaction time of 0.75 seconds. Since your car is traveling at a constant speed of 16 m/s, we can use a simple formula: distance = speed x time.

distance = 16 m/s x 0.75 seconds = 12 meters

Therefore, your car will cover a distance of 12 meters while your brain is figuring out what to do.

c) If you decide that braking is in your best interest, how long will it take you to come to a complete stop once you begin the process of braking?

To answer this question, we need to calculate the time it takes for your car to come to a complete stop using the maximum acceleration of 6.0 m/s^2.

We can use the formula: time = velocity change / acceleration.

Since your car is currently traveling at a speed of 16 m/s, and you need to stop, the velocity change is 16 m/s.

time = 16 m/s / 6.0 m/s^2 = 2.67 seconds

Therefore, it will take approximately 2.67 seconds for your car to come to a complete stop if you decide to brake.

d) What is the minimum distance you must be from the truck to successfully stop before hitting it?

To calculate the minimum distance to stop before hitting the truck, we need to consider the distance traveled during your reaction time and the distance required to come to a complete stop.

The total distance required is the sum of the distance traveled during your reaction time and the distance traveled while stopping.

Total distance = distance during reaction time + distance to come to a complete stop

Total distance = 12 meters + 16 meters (distance traveled during braking)

Total distance = 28 meters

Therefore, you must be at least 28 meters away from the truck to successfully stop before hitting it.