Assume the truck is going at v0 = 25 m/s, and you're 20 m behind the truck. You decide to accelerate at a = 1.0 m/s2 to pass the truck. To pass safely, you also want to pass the truck by 20 m before moving back to the lane.

Part A ) Estimate the time interval needed to pass a semi-trailer truck on a highway.
Part B) If you are on a two-lane highway, how far away from you must an approaching car be in order for you to safely pass the truck without colliding with the oncoming traffic? Assume the speed of an approaching car is also 25 m/s.

Part A) To estimate the time interval needed to pass the semi-trailer truck, we can use the equation of motion:

v = v0 + at,

where v is the final velocity, v0 is the initial velocity, a is the acceleration, and t is the time.

Given:
v0 = 25 m/s,
a = 1.0 m/s².

Since the truck is moving at a constant velocity, its final velocity v remains 25 m/s.

To calculate the time needed to accelerate and pass the truck, we can rearrange the equation:

t = (v - v0) / a.

Substituting the given values into the equation:

t = (25 m/s - 0 m/s) / (1.0 m/s²).

Simplifying:

t = 25 s.

Therefore, it would take approximately 25 seconds to pass the truck.

Part B) To determine the safe distance from an approaching car on a two-lane highway, we need to consider the time it takes for the car to reach the point where you will return to your lane after passing the truck.

The total time needed to pass the truck is 25 seconds, as calculated in Part A. During this time, both you and the approaching car will travel at a speed of 25 m/s.

To find the distance covered by the car during this time, we can use the equation:

s = vt,

where s is the distance, v is the velocity, and t is the time.

Substituting the values:

s = 25 m/s * 25 s.

Simplifying:

s = 625 m.

Therefore, the approaching car must be at least 625 meters away from you to safely pass the truck without colliding with oncoming traffic.

To solve these problems, we can use the equations of motion. Let's break down the steps to find the answers for Part A and Part B.

Part A) Estimate the time interval needed to pass a semi-trailer truck on a highway.

Step 1: Calculate the initial distance between the truck and you:
The truck is 20 m ahead of you initially.

Step 2: Calculate the final distance you want to be ahead of the truck:
You want to be 20 m ahead of the truck after passing it.

Step 3: Calculate the relative velocity between you and the truck:
The relative velocity is the difference between your velocity and the truck's velocity. In this case, since your velocity is 25 m/s and the truck's velocity is assumed to be constant, the relative velocity is 0.

Step 4: Use the equation of motion to calculate the time needed to pass the truck:
The equation of motion we will use is:
distance = initial velocity * time + 0.5 * acceleration * time^2

Since the final distance you want to be ahead of the truck is 20 m, the initial velocity is 0 (relative velocity is 0), and the acceleration is 1.0 m/s^2 (your acceleration to pass the truck), the equation becomes:
20 = 0 * time + 0.5 * 1.0 * time^2

Simplifying the equation gives:
10 * time^2 = 20

Solving for time:
time^2 = 20 / 10
time^2 = 2
time = sqrt(2) (taking the positive square root as time cannot be negative)

Therefore, the estimated time interval needed to pass the truck is approximately sqrt(2) seconds.

Part B) If you are on a two-lane highway, how far away from you must an approaching car be in order for you to safely pass the truck without colliding with the oncoming traffic? Assume the speed of an approaching car is also 25 m/s.

To calculate this, we need to consider the distance covered while passing the truck and the relative distance from the approaching car.

Step 1: Calculate the distance covered while passing the truck:
We already know that the initial distance between you and the truck is 20 m, and the final distance you want to be ahead of the truck is also 20 m. So the total distance covered while passing the truck is twice the distance you want to be ahead, which is 40 m (20 m + 20 m).

Step 2: Calculate the relative distance from the approaching car:
The approaching car is moving towards you with a speed of 25 m/s. To safely pass without colliding, you should create a distance equal to the sum of the distance traveled while passing the truck and the current distance between you and the truck.

Relative distance = Distance covered while passing the truck + Initial distance between you and the truck
Relative distance = 40 m + 20 m
Relative distance = 60 m

Therefore, the approaching car must be at least 60 m away from you to safely pass the truck without colliding with the oncoming traffic.

so you want to move 40 meters (assuming the truck has no length) with a relative velocity of V with acceleration = 1.0m/s^2

distance=at
40=1t time = 40 seconds
so you are in the wrong lane for 40 seconds, and the relative speed of the oncoming cars is 50m/s

distance=v*t=50*40=2000 m

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