Question

the speed of a falling object increases at a constant rate as time increases since the object was dropped. which graph could represent the relationship between \\(t\\), time in seconds, and \\(s\\), speed in meters per second?

Explanation:

Analyze the rate of change

Using the Function Modeling knowledge point

• The problem states that the speed increases at a "constant rate" over time.
• A constant rate of change represents a linear relationship, which is graphed as a straight line.

Identify the initial state

• The object is "dropped", meaning its initial speed at time \(t = 0\) is \(s = 0\).
• The graph must start at the origin \((0, 0)\).

Evaluate the graph options

• Graph 1 (top-left) shows an increasing curve that is not straight (exponential or quadratic growth).
• Graph 2 (top-middle) shows a straight line of points starting at \((0,0)\) and increasing at a constant rate.
• Graph 3 (top-right) shows a decreasing curve.
• Graph 4 (bottom-left) shows a decreasing straight line.
• Therefore, the second graph (top-middle) correctly represents the relationship.

Answer:

• (A) Graph showing an upward curve starting at (0,0)
• (B) Graph showing a straight line of points increasing from (0,0) (Correct answer)
• (C) Graph showing a downward curve
• (D) Graph showing a straight line of points decreasing