Calculating Athlete's Speed in km/h
The question asks for the speed of an athlete in kilometers per hour (km/h), given the distance run and the time taken.
Distance = 300 meters
Time = 24 seconds
Step 1: Calculate Speed in Meters per Second (m/s)
First, find the speed using the formula: Speed = Distance / Time.
$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $
Substitute the given values:
$ \text{Speed} = \frac{300 \text{ m}}{24 \text{ s}} $
Simplify the fraction:
$ \text{Speed} = 12.5 \text{ m/s} $
Step 2: Convert Speed to Kilometers per Hour (km/h)
To convert speed from meters per second (m/s) to kilometers per hour (km/h), multiply by the conversion factor $ \frac{18}{5} $.
$ \text{Speed (km/h)} = \text{Speed (m/s)} \times \frac{18}{5} $
Apply the conversion:
$ \text{Speed (km/h)} = 12.5 \times \frac{18}{5} $
Calculate the result:
$ \text{Speed (km/h)} = \frac{25}{2} \times \frac{18}{5} = \frac{5 \times 18}{2} = 5 \times 9 = 45 \text{ km/h} $
The athlete's speed is 45 km/h.
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