In which of the following examples will an athlete have a maximum accelerated motion?
Running on a circular track
Understanding Accelerated Motion for Athletes
To understand where an athlete experiences maximum accelerated motion, we need to define acceleration. Acceleration is the rate of change of velocity. Velocity is a vector quantity, meaning it has both magnitude (speed) and direction. Therefore, acceleration can occur in two ways:
- If the speed changes (increases or decreases).
- If the direction of motion changes, even if the speed remains constant.
Athlete's Motion on Different Tracks
Let's consider an athlete running at a relatively constant speed on different types of tracks:
| Track Shape | Path Description | Change in Direction | Acceleration |
|---|---|---|---|
| Rectangular Track | Straight sections and sharp 90-degree corners. | Changes abruptly only at the four corners. | Approximately zero during straight sections (if speed is constant). High instantaneous acceleration at corners as direction changes rapidly. |
| Hexagonal Track | Straight sections and six corners with turns. | Changes abruptly only at the six corners. | Approximately zero during straight sections. Instantaneous acceleration at corners. The turns are less sharp than a rectangle's 90 degrees. |
| Octagonal Track | Straight sections and eight corners with turns. | Changes abruptly only at the eight corners. | Approximately zero during straight sections. Instantaneous acceleration at corners. The turns are less sharp than a hexagon's turns. |
| Circular Track | Continuously curved path. | Changes continuously at every point along the track. | Constant centripetal acceleration towards the center, even if speed is constant. The magnitude of this acceleration is given by $\text{a}_\text{c} = \frac{\text{v}^2}{\text{r}}$, where $\text{v}$ is the speed and $\text{r}$ is the radius. |
Why a Circular Track Causes Maximum Accelerated Motion
The question asks for the scenario with maximum accelerated motion. On polygonal tracks (rectangular, hexagonal, octagonal), the athlete experiences significant acceleration primarily at the corners where they change direction. Between corners, on the straight sections, if the athlete maintains a constant speed, the acceleration is close to zero.
On a circular track, however, the direction of the athlete's velocity is constantly changing as they move around the curve. This continuous change in direction means there is always an acceleration, specifically a centripetal acceleration directed towards the center of the circle. This acceleration is constant in magnitude (if speed is constant) and always perpendicular to the velocity.
As the number of sides of a regular polygon increases, the polygon's shape gets closer and closer to a circle. The corners become more numerous but less sharp. In the limit, a circle can be thought of as a polygon with an infinite number of infinitesimally small sides, where the "corners" are everywhere, leading to continuous change in direction and thus continuous acceleration.
Therefore, running on a circular track involves continuous acceleration due to the constant change in direction, providing a state of maximum sustained or continuous accelerated motion compared to the intermittent acceleration experienced at the corners of polygonal tracks.
Conclusion
An athlete running on a circular track experiences continuous centripetal acceleration because their direction of motion is constantly changing. On polygonal tracks, acceleration occurs mainly at the corners. Thus, the circular track provides the scenario with maximum accelerated motion.
Revision Table: Track Acceleration Analysis
| Track Type | Nature of Acceleration | Is Acceleration Continuous? |
|---|---|---|
| Rectangular | Mostly instantaneous at corners | No |
| Hexagonal | Mostly instantaneous at corners | No |
| Octagonal | Mostly instantaneous at corners | No |
| Circular | Continuous (centripetal) | Yes |
Additional Information: Centripetal Force and Motion
The acceleration experienced on a circular track is called centripetal acceleration. This acceleration is always directed towards the center of the circle. According to Newton's second law, a force is required to cause this acceleration. This force is called the centripetal force, and it is also directed towards the center. For an athlete running on a track, the centripetal force is provided by the friction between their shoes and the track surface, and also by the athlete leaning into the turn.
Understanding centripetal acceleration is crucial in physics when studying circular motion. It explains why objects moving in a circle, even at constant speed, are constantly accelerating and therefore require a net force acting on them.
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