Question

A commuter train travels from Baltimore to Washington DC and back in 1 hour and 45 minutes. The distance between these two stations is about 40 miles. a.) What is the average velocity of the train?b.) What is the average speed of the train in m/s? Please provide a detailed explanation.

Answer 1

The average velocity of the train is zero since it returns to the starting point, resulting in zero displacement. The average speed of the train is approximately 45.71 mph, or 20.41 m/s, calculated over a round-trip distance of 80 miles and a duration of 1 hour and 45 minutes.

Step-by-step explanation:

The student asked about the average velocity and average speed of a commuter train traveling between Baltimore and Washington, DC. To calculate the average velocity, we consider the displacement and the total time taken for the round trip. Since the train returns to its starting point, the displacement is zero, and therefore the average velocity is also zero.

For the average speed, we need to consider the total distance traveled and the total time taken. The train travels 40 miles to Washington, DC, and then 40 miles back to Baltimore, making a total distance of 80 miles. The time taken for the trip is 1 hour and 45 minutes, which is equivalent to 1.75 hours or 6300 seconds. The average speed (in miles per hour) is the total distance divided by the total time:

Speed = Total distance / Total time = 80 miles / 1.75 hours = approximately 45.71 mph

To convert this to meters per second (m/s), we use the conversion factor where 1 mile = 1609.34 meters and 1 hour = 3600 seconds.

Speed in m/s = (45.71 miles/hour) * (1609.34 meters/mile) / (3600 seconds/hour) = approximately 20.41 m/s

Thus, the average speed of the train is approximately 20.41 m/s.

Answer 2

Answer:a) 0 b) 47.5mi/h

Explanation:

velocity is vector so you have to consider magnitude and direction

speed is the magnitude of your vector velocity so is just a number not a vector.

time of travel t = 1h+ 45min = 1h + 0.75h = 1.75h

the average speed (constant) is simply v= d/t = ( 2*40 ) /1.75 =45.7mi/h

because we travel 40miles two times so the distance is 80mi.

but the average velocity (two tracks) is clearly zero because here you have to consider the train direction and in both directions the speed is the same but the direction opposite.... so if the speed vectors give sum zero