Question

A roller coaster moves along an inclined linear path before it reaches its maximum height. The car moves at a constant speed and gains 4 meters in height every 3 seconds.

The slope of the line that represents the height of the car in meters in terms of time in seconds is ______

Answer 1

The slope of the line representing the height of the roller coaster in terms of time is 4/3 meters per second, as it gains 4 meters in height every 3 seconds.

Step-by-step explanation:

The question regards the rate of height gain of a roller coaster that is moving up an incline at a constant speed. To find the slope of the line that represents the height of the car in terms of time, we can use the given information that the roller coaster gains 4 meters in height every 3 seconds.

Since slope is defined as the ratio of the rise over the run, in this case, the change in height over the change in time, we can express it as:

Slope = Change in Height / Change in Time = 4 meters / 3 seconds = 4/3 meters per second (m/s).

Therefore, the slope of the line that represents the height of the car as a function of time is 4/3 m/s.

The slope of the line that represents the height of the car in meters in terms of time in seconds can be determined using the formula for slope, which is rise over run. In this case, the car is gaining 4 meters in height every 3 seconds, so the rise is 4 meters and the run is 3 seconds. Therefore, the slope is 4/3 or 1.33.