In 1954, Roger Bannister became the first human to run a mile in less than 4 minutes. Suppose that a runner on a straight track covers a distance of 1.00 mi in exactly 4.00 min.
1. What is his average speed in mi/h?
2. What is his average speed in ft/s?
3. What is his average speed in m/s?
1.00 mi in 4.00 min
1 mile/min = 60 mph
1 mile/4 min = 0.25 mi/min
1. 0.25 x 60 mi/hr = ? mph
2. 0.25 x 88 ft/sec = ? ft/sec
3. 0.25 x 26.8224 meters/sec = ? meters/sec
should have added above,
1 mi = 5280 feet
1 mi = 1609.344 meters
1 mi/min = 60 mi/hr
1 mi/min = 88 ft/sec
1 mi/min = 26.8224 meters/sec
sorry for the confusion. I wish there was a 'do over' button. :)
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To solve these questions, we can use the equation:
average speed = total distance ÷ total time
1. To find the average speed in mi/h, we divide the total distance, which is 1.00 mi, by the total time, which is 4.00 min. First, we need to convert the time to hours since the distance is given in miles:
total time = 4.00 min = 4.00 ÷ 60 = 0.067 hours
Now, we can calculate the average speed:
average speed = 1.00 mi ÷ 0.067 hours ≈ 14.93 mi/h
Therefore, the runner's average speed is approximately 14.93 mi/h.
2. To find the average speed in ft/s, we need to convert the distance and time to consistent units. Since 1 mile is equal to 5,280 feet, we can calculate:
total distance in feet = 1.00 mi × 5,280 ft/mi = 5,280 ft
total time in seconds = 4.00 min × 60 s/min = 240 s
Now, we can calculate the average speed:
average speed = 5,280 ft ÷ 240 s ≈ 22 ft/s
Therefore, the runner's average speed is approximately 22 ft/s.
3. To find the average speed in m/s, we again need to convert the distance and time to consistent units. Since 1 mile is equal to 1.60934 kilometers (km) and 1 km is equal to 1,000 meters (m), we can calculate:
total distance in meters = 1.00 mi × 1.60934 km/mi × 1,000 m/km = 1,609.34 m
total time in seconds = 4.00 min × 60 s/min = 240 s
Now, we can calculate the average speed:
average speed = 1,609.34 m ÷ 240 s ≈ 6.705 m/s
Therefore, the runner's average speed is approximately 6.705 m/s.