What is the speed $ v $ of an athlete, if the athlete takes $ t $ seconds to go once around a circular path of

Question

What is the speed $ v $ of an athlete, if the athlete takes $ t $ seconds to go once around a circular path of radius $ r $?

Examoogle · Accepted Answer

The correct answer is Option A: $v = \frac{2\pi r}{t}$. The speed of an object moving in a circle is defined as the total distance covered in one revolution divided by the time taken. For a circular path with radius $r$, the distance covered in one full trip is the circumference of the circle, which is given by $2 \pi r$.

Step-by-Step Solution & Concepts:
The speed of an object moving in a circle is defined as the total distance covered in one revolution divided by the time taken. For a circular path with radius $r$, the distance covered in one full trip is the circumference of the circle, which is given by $2 \pi r$.

Working Principle: In uniform circular motion, speed ($v$) is calculated as the ratio of the distance traveled ($d$) along the path to the time interval ($t$). Since one complete round follows the perimeter of the circle, the distance $d = 2 \pi r$. Thus, the expression becomes $v = \frac{2 \pi r}{t}$.

Key Formulas: $v = \frac{2 \pi r}{t}$ — Speed formula for one circular revolution; $C = 2 \pi r$ — Circumference of a circle

Key Points: Speed is a scalar quantity while velocity in circular motion changes direction constantly.; The SI unit of speed is meters per second (m/s).; One complete revolution corresponds to an angle of $2 \pi$ radians.

Advantages: Simple derivation based on basic kinematics.

Applications: Calculating orbital speed of satellites.; Determining the speed of athletes on a track.

Additional Info: The value $\pi \approx 3.14159$.. Option B (2 m/s) is a numerical example, not a formula.. Option C (0) represents an object at rest or a scenario with zero displacement, but speed is non-zero if motion occurs.. Option D ($\pi r^2/t$) incorrectly uses the area of a circle instead of the circumference.

Answer: A is correct — The speed $v$ is the ratio of the total distance $2 \pi r$ covered in one revolution to the time $t$ taken.

Exam Tip: Always ensure the units in your physics problems match (e.g., $r$ in meters, $t$ in seconds) to yield $v$ in $m/s$.

Examoogle · Answer

Option B: $v = 2\,m/s$

Examoogle · Answer

Option C: $v = 0$

Examoogle · Answer

Option D: $v = \frac{\pi r^2}{t}$

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