A runner times his speed around a track with a circumference of 0.50 mi . He finds that he has r

step 1 In the given problem, circumference of a track is given as 0 .50 miles. The circumference of thi

A runner times his speed around a track with a circumference...

A runner times his speed around a track with a circumference of $0.50 \mathrm{mi} .$ He finds that he has run a distance of $1.00 \mathrm{mi}$ in 4.0 min. What is his (a) average speed and
(b) average velocity magnitude in $\mathrm{m} / \mathrm{s}$ ?

Key Concepts

Average Speed

Average speed is defined as the total distance traveled divided by the total time taken. It is a scalar quantity, which means it only carries a magnitude and no directional information. In problems of motion, calculating average speed involves summing up all segments of the path regardless of the direction, then dividing by the elapsed time to yield a rate of travel.

Average Velocity

Average velocity is defined as the displacement (the change in position) divided by the total time taken. It is a vector quantity, meaning it has both magnitude and direction. In uniform circular or closed-loop motion, even though the average speed may be non-zero, the average velocity can be lower (or even zero) if the starting and ending points are the same.

Displacement versus Distance

Distance is the total length of the path traveled, irrespective of direction, whereas displacement refers to the change in position between the start and end points. This difference is critical in physics, especially when comparing average speed (which uses distance) and average velocity (which uses displacement).

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In problems involving speed and velocity, it is often necessary to convert units such as miles to meters or minutes to seconds to ensure consistency, especially when the answer is required in SI units like meters per second (m/s).

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