The first part of this question requires you to know the definition of velocity:
a) Velocity, in this case, is defined as distance traveled over a period of time (distance/time).
The runner moves a distance of 23.5 miles in 2 hours. The velocity of the runner is therefore (23.5 miles)/(2 hours), which is equal to 11.75 miles/hour.
The second part of this question requires you to know the conversion between miles and meters and hours and seconds:
b) Meters are a unit of measurement, meaning that they have a direct conversion value to miles. That number is 1609.344 meters to 1 mile.
We now need the number of seconds in an hour. This conversion is well-known. There are sixty minutes in an hour and sixty seconds in a minute. This means that the number of seconds in an hour is (60 x 60) or 3600 seconds.
Now that we have the number of meters in a mile and the number of seconds in an hour, we are ready to convert our equation.
(11.75 miles/hour) * (1609.344 meters/1 mile) * (1 hour/3600 seconds) = 5.25 meters/second.
First, let us find the runner's velocity in miles per hour. The velocity v can be found as the distance by the time during which the distance was traveled:
v = 23.5/2 = 11.75 miles per hour (mph).
To convert the velocity from the miles per hour to meters per second, consider that 1 mile = 1.6093 kilometers = 1609.3 meters and
1 hour = 60 minutes = 60*60 = 3600 seconds.
Then, 11.75 mph = 11.75* (1609.3 m)/(3600 s) = 5.253 m/s
So, if the runner covers a distance of 23.5 miles in 3 hours, his velocity in meters per second is 5.253 m/s.
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