Final answer:
The distance travelled is proportional to time for a person running on a treadmill at 3 mph for 6 minutes because the treadmill represents a controlled environment where speed is constant, creating a direct proportional relationship between distance and time.
Step-by-step explanation:
In which situation is the distance travelled proportional to time? The correct answer is a person running on a treadmill at 3 mph for 6 minutes. This scenario describes a condition of constant velocity where the person runs at a steady rate of 3 miles per hour (mph) for a fixed time period. According to the definition of velocity, which is the rate of change of distance with respect to time, a constant velocity implies a direct proportional relationship between distance and time. The treadmill ensures a controlled environment with the absence of external factors that might influence the runner's speed. Therefore, as time passes, the distance increases by a constant amount.
Looking at the other options: An aeroplane landing involves deceleration, as does a roller coaster ride which also includes varying speeds. A soccer ball kicked across a field is affected by external forces such as air resistance and friction which cause the ball to eventually come to a stop, meaning its velocity is not constant.
To further illustrate the concept of proportionality in motion, we could consider an athlete on a treadmill who travels a certain distance in one minute. Since the speed is constant, doubling or tripling the time spent running would result in doubling or tripling the distance travelled, so if 10 km is travelled in 20 minutes, then in one hour (which is three times 20 minutes), the distance would be 10 km times 3, which is 30 km. This example emphasizes the consistent and predictable relationship between time and distance when moving at a constant velocity.