To sketch a graph for the function that models the relationship between distance (d) and velocity (v) in this scenario, we would first plot the points (0,0), (3,3), (12,6), and (27,9) on a coordinate plane. These points correspond to the values of distance and velocity from the experiment.
Next, we would draw a smooth curve through these points to represent the square root function that models the relationship between d and v. This curve would start at the origin (0,0) and increase as the distance traveled increases. Since the relationship is modeled by a square root function, the curve will not increase linearly, but rather at a slower rate as the distance traveled increases.
The resulting graph would curve upwards, getting closer and closer to a straight line as the distance traveled and velocity increase. This graph visually represents how the velocity of the air particle increases as it travels further distances, according to the relationship modeled by the square root function.
The relationship between the distance an air particle has traveled (d) and its velocity (v) can be modeled by the square root function. The values of d and v from an experiment are recorded in the table below.
d (meters) 0 3 12 27
v ( meters per second ) 0 3 6 9
Explain in words how to sketch a graph for the function that models this relationship.
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