A polar bear can run at a rate of 25 mph for short bursts. However, it can travel at a rate of 15 mph for longer periods of time. Which graph represents the distance a polar bear can travel for longer periods of time?
Responses
Since the bear can travel at a rate of 15 mph for longer periods of time, the graph representing this would be a straight line at a constant distance of 15 miles per hour. This indicates that the distance traveled is the same for every unit of time.
The correct graph would be a horizontal line at a distance of 15 miles per hour.
To determine which graph represents the distance a polar bear can travel for longer periods of time, we need to compare the rates at which it can travel.
Graph A) shows a constant distance covered over time, which indicates a constant rate of travel. This does not represent the varying rates of a polar bear.
Graph B) shows an increasing distance covered over time, which indicates an acceleration. This also does not represent the constant rate of a polar bear.
Graph C) shows a straight line with a constant slope, indicating a constant rate of travel. This represents the polar bear's ability to travel at a rate of 15 mph for longer periods of time.
Therefore, the correct graph that represents the distance a polar bear can travel for longer periods of time is Graph C.
To determine which graph represents the distance a polar bear can travel for longer periods of time, we need to find the relationship between speed and time for this specific situation.
The question states that the polar bear can travel at a rate of 15 mph for longer periods. This means that the distance covered will vary depending on the time duration.
We can use the formula distance = speed × time to calculate the distance covered. Rearranging the formula, we have time = distance / speed.
Since the speed is constant at 15 mph, the time taken will directly depend on the distance covered. For example, if the bear travels at a speed of 15 mph for 1 hour, it will cover a distance of 15 miles. Similarly, if it travels for 2 hours, it will cover a distance of 30 miles.
Now let's analyze the graph options:
1. Graph A: This graph shows a straight line with a positive slope. As time increases, the distance increases steadily. This represents a constant speed travel and does not match the scenario of a polar bear traveling at 15 mph for longer periods.
2. Graph B: This graph shows a curve that is steeper at the beginning and gradually becomes less steep over time. The distance increases rapidly initially, but the rate of increase decreases as time progresses. This kind of graph doesn't match the situation of a polar bear traveling at a constant speed for longer periods.
3. Graph C: This graph shows a horizontal line, indicating that the distance covered does not change with time. This scenario does not correspond to the given information about the polar bear's speed.
4. Graph D: This graph shows a curved line that initially increases steeply but becomes less steep as time goes on. This curve represents a situation where the distance increases rapidly initially and then increases at a slower rate as time progresses. This matches the situation of a polar bear traveling at a speed of 15 mph for longer periods of time, as it matches the scenario described in the question.
Therefore, graph D represents the distance a polar bear can travel for longer periods of time.