IF A TORTOISE AND A HARE ARE RUNNING IN A RACE. AND IN MY GRAPH I HAVE DISTANCE IN THE VERTICAL SCALE AND TIME IN THE HORIZONTAL SCALE. THE TORTOISE IS RUNNING AT A CONSTANT RATE WITHOUT STOPPING. BUT THE HARE IS CONFIDENT AND HE STOPS HOPPING AND WAITS FOR THE TORTOISE TO ALMOST CATCH UP AND THEN STARTS HOPPING AGAIN. DURING THE TIME THE HARE HAD STOPPED WHAT IS WOULD THE SLOPE OF HIS LINE BE IN MY GRAPH?
Zero slope at those times. Hare's complete graph would be a series of steps with flat tops and slanted upward-sloping sides.
To determine the slope of the hare's line during the time it had stopped hopping, we need to understand the concept of slope and how it relates to a graphical representation of the race.
In your graph, with distance on the vertical scale and time on the horizontal scale, the slope represents the rate at which the distance changes with respect to time. Mathematically, the slope can be calculated as the change in distance divided by the change in time (Δy/Δx).
Let's break down the situation into different segments:
1. Tortoise running at a constant rate: Since the tortoise is running at a constant rate without stopping, its line on the graph will be represented by a straight line with a constant slope. This slope will be determined by the tortoise's running speed.
2. Hare stopping and starting: The hare's line on the graph will consist of two segments - one with a positive slope when the hare is hopping, and another with a slope of zero when the hare stops. During the time the hare had stopped hopping, the distance did not change, but the time continued to progress. Therefore, the change in distance Δy will be zero, while the change in time Δx will be non-zero.
When Δy is zero, the slope becomes 0/Δx, which is equivalent to 0. Hence, the slope of the hare's line during the time it had stopped hopping will be zero.
So, during the time the hare had stopped hopping, the slope of its line on your graph would be zero.