6. a roller - coaster ride runs in the same pattern. at first, it climbs a hill at a slow, constant rate…

6. a roller - coaster ride runs in the same pattern. at first, it climbs a hill at a slow, constant rate. then it moves quickly down the first hill, begins to slow as it ascends the second hill, speeds up again down the second hill, and slows at a constant speed until the ride ends at the starting gate. sketch a qualitative graph to represent the situation.

6. a roller - coaster ride runs in the same pattern. at first, it climbs a hill at a slow, constant rate. then it moves quickly down the first hill, begins to slow as it ascends the second hill, speeds up again down the second hill, and slows at a constant speed until the ride ends at the starting gate. sketch a qualitative graph to represent the situation.

Answer

Explanation:

Step1: Analyze the first part

The roller - coaster climbs a hill at a slow, constant rate. So, the graph will be a straight line with a positive slope (since the height is increasing) and a relatively small slope value.

Step2: Analyze the second part

It moves quickly down the first hill. So, the graph will be a straight line with a negative slope (height is decreasing) and a relatively large slope value (because it's moving quickly).

Step3: Analyze the third part

Begins to slow as it ascends the second hill. So, the graph will be a curve (since the rate of change of height is decreasing) with a positive slope (height is increasing).

Step4: Analyze the fourth part

Speeds up again down the second hill. So, the graph will be a curve (since the rate of change of height is increasing) with a negative slope (height is decreasing).

Step5: Analyze the fifth part

Slows at a constant speed until the ride ends. So, the graph will be a straight line with a negative slope (height is decreasing) and a relatively small slope value (constant slow speed).

Answer:

The graph will start with a straight line with a small positive slope (climbing the first hill), then a straight line with a large negative slope (descending the first hill), followed by a curve with a positive slope (ascending the second hill, slowing), then a curve with a negative slope (descending the second hill, speeding up), and finally a straight line with a small negative slope (slowing to a stop at the starting gate).