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
It is easier to solve this problem if we introduce the relative velocity of the car (relative to the train). The velocity of the car relative to the train is (95-75) km/h=20 km/h.
In the relative description the train is not moving and the car is moving with constant speed 20 km/h.
a. The time the car needs to pass the train is
t = length of the train/relative speed = 1.1 km/20 (km/h) = 0.055 h =198 s.
b. To find the actual traveled distance of the car we just need to multiply the traveled time (0.055 h) by the actual speed of the car:
L = 95•0.055 = 5.225 km
c. The relative speed is v1= 95+75 =170 km/h
The time the car needs to pass the train in this case is
t1= length of the train/relative speed v1= 1.1 km/170 (km/h)=
= 0.00647h =23.3 s.
d. To find the actual traveled distance of the car we just need to multiply the traveled time (0.00647 h) by the actual speed of the car:
L = 95•0.00647 = 0.615 km.
very Understandable
Q1: To find the time it takes for the car to pass the train, we can use the relative speed between the two. Since they are traveling in the same direction, the relative speed is the difference between their speeds:
Relative speed = car's speed - train's speed = 95 - 75 = 20 mph.
To find the time, we can use the formula: Time = Distance / Speed.
Since we know the length of the train is 1.10 miles, we can substitute the values into the formula:
Time = 1.10 miles / 20 mph = 0.055 hours (or 3.3 minutes).
Therefore, it takes the car approximately 3.3 minutes to pass the train.
Q2: To find how far the car will have traveled in this time, we can use the formula: Distance = Speed x Time.
Since the car's speed is 95 mph and the time is 0.055 hours, we can calculate the distance:
Distance = 95 mph x 0.055 hours = 5.225 miles.
Therefore, the car will have traveled approximately 5.225 miles.
Q3: If the car and train are traveling in opposite directions, their speeds should be added together to find the relative speed:
Relative speed = car's speed + train's speed = 95 + 75 = 170 mph.
Using the same formula, Time = Distance / Speed, and knowing that the distance is 1.10 miles:
Time = 1.10 miles / 170 mph = 0.00647 hours (or approximately 0.388 minutes).
Therefore, it takes the car approximately 0.388 minutes to pass the train when they are traveling in opposite directions.
Q4: When the car and train are traveling in opposite directions, we can calculate the total distance covered by the car by adding up the distances traveled by each object separately.
Distance = car's speed x Time + train's speed x Time = (95 mph x 0.00647 hours) + (75 mph x 0.00647 hours)
Distance = (0.61565 miles) + (0.4875 miles) = 1.10315 miles.
Therefore, the car will have traveled approximately 1.10315 miles when the car and train are traveling in opposite directions.
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.