To answer these questions, we need to understand the concepts of relative speed, time, and distance.
Relative speed is the difference between the velocities of two objects that are moving in the same or opposite directions. It is calculated by subtracting the slower velocity from the faster one.
Q1: To find how long it takes for the car to pass the train, we need to determine the relative speed between them. Since they are moving in the same direction, the relative speed is the difference between the car's velocity and the train's velocity. So, the relative speed would be 95 - 75 = 20 mph. Now, we can use the formula:
time = distance / speed
Since the train is 1.10 miles long, the time it takes for the car to pass it would be:
time = 1.10 / 20 = 0.055 hours or 3.3 minutes.
Q2: To find how far the car will have traveled in this time, we can multiply the car's velocity by the time it takes to pass the train. The car's velocity is 95 mph, and the time from Q1 is 0.055 hours. Hence, the distance the car will have traveled is:
distance = velocity * time
distance = 95 * 0.055 = 5.225 miles.
Q3: When the car and train are traveling in opposite directions, we need to calculate the sum of their velocities (since they are moving away from each other). The relative speed in this case would be:
relative speed = car's velocity + train's velocity
relative speed = 95 + 75 = 170 mph.
Again, we can use the formula:
time = distance / speed
Since the train is 1.10 miles long, the time it takes for the car to completely overtake the train would be:
time = 1.10 / 170 = 0.0065 hours or 0.39 minutes.
Q4: To find how far the car will have traveled in this time, we can multiply the car's velocity by the time it takes to overtake the train. The car's velocity is 95 mph, and the time from Q3 is 0.0065 hours. Hence, the distance the car will have traveled is:
distance = velocity * time
distance = 95 * 0.0065 ≈ 0.6175 miles.
So, to summarize:
- The car takes approximately 3.3 minutes to pass the train if they are traveling in the same direction.
- The car travels approximately 5.225 miles in that time.
- If the car and train are traveling in opposite directions, it takes approximately 0.39 minutes for the car to overtake the train completely.
- The car travels approximately 0.6175 miles in that time.