An automobile traveling 95 overtakes a 1.10--long train traveling in the same direction on a track parallel to the road.
Q1: If the train's speed is 75 , how long does it take the car to pass it
Q2:How far will the car have traveled in this time?
Q3:What is the time if the car and train are traveling in opposite directions?
Q4:How far will the car have traveled if the car and train are traveling in opposite directions
I want the answer
To answer these questions, we can use the formula for relative speed and distance. The relative speed is the difference between the speeds of the car and the train.
Q1: To find the time it takes for the car to pass the train, we need to calculate the distance traveled by the car relative to the train. Given that the train is 1.10 meters long and the car's speed is 95 m/s while the train's speed is 75 m/s, the relative speed is 95 m/s - 75 m/s = 20 m/s.
The time it takes for the car to pass the train can be calculated using the formula:
Time = Distance / Speed
Since the car needs to travel a distance equal to the length of the train (1.10 m) relative to the train's speed (20 m/s), we can calculate:
Time = 1.10 m / 20 m/s = 0.055 seconds
Therefore, it takes the car 0.055 seconds to pass the train.
Q2: The distance traveled by the car in this time can be calculated using the formula:
Distance = Speed * Time
Using the car's speed of 95 m/s and the time calculated in Q1 (0.055 seconds), we can calculate:
Distance = 95 m/s * 0.055 seconds = 5.225 meters
Therefore, the car will have traveled approximately 5.225 meters in the time it takes to pass the train.
Q3: If the car and train are traveling in opposite directions, their velocities are added together. So the relative speed is:
Relative speed = Car's speed + Train's speed = 95 m/s + 75 m/s = 170 m/s
To find the time in this case, we use the same formula:
Time = Distance / Speed
Since the distance is still 1.10 meters, we can calculate:
Time = 1.10 m / 170 m/s ≈ 0.00647 seconds
Therefore, the time taken for the car to pass the train when they are traveling in opposite directions is approximately 0.00647 seconds.
Q4: Similarly, when the car and train are traveling in opposite directions, their velocities are added together. So the relative speed is:
Relative speed = Car's speed + Train's speed = 95 m/s + 75 m/s = 170 m/s
To find the distance traveled by the car in this time, we use the formula:
Distance = Relative speed * Time
Using the relative speed of 170 m/s and the time calculated in Q3 (0.00647 seconds), we can calculate:
Distance = 170 m/s * 0.00647 seconds = 1.0979 meters
Therefore, the car would have traveled approximately 1.0979 meters when the car and train are traveling in opposite directions.