A runner runs 100 meters in 12 seconds and we are asked to find the average speed.

The average speed is the total distance divided by the total time over some interval. This is the rate of change of distance with respect to time. Here the average speed is given...

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A runner runs 100 meters in 12 seconds and we are asked to find the average speed.

The average speed is the total distance divided by the total time over some interval. This is the rate of change of distance with respect to time. Here the average speed is given by (100m)/(12s) or 8 & 1/3 m/s, or 8.33.

**The average speed is 8 and 1/3 m/s.**

This can be converted to other units such as km/hr or miles per hour:

(a) km/hr: 25/3 m/s * 1/1000 km/m * 3600/1 s/hr = 30 km/hr

(b) mi/hr: 25/3 m/s * 3600/1 s/hr * 100 cm/m * 1/2.54 in/cm *1/12 ft/in*1/5280 mi/ft = 18.64 mi/hr

In general speed can be thought of as the rate, where d=rt with d the distance traveled, r the rate, and t the time. So, we have 100m=r(12s), so r=100/12 m/s or 8 and 1/3 m/s.