Question

learn sketch qualitative graphs qualitative graphs represent essential elements of a situation in a graphical form. you can sketch qualitative graphs to represent many real - world functions that are described verbally. charlie’s speed over time: charlie is riding his bike. he speeds up, rides at a consistent speed, then slows down. sketch a qualitative graph to represent the scenario.

Explanation:

Step1: Analyze the scenario phases

Charlie's bike ride has three phases: speeding up (speed increases with time), constant speed (speed is constant as time passes), and slowing down (speed decreases with time).

Step2: Map phases to graph segments

• Speeding up: The graph segment should have a positive slope (since speed \( s \) increases as time \( t \) increases, so \( \frac{ds}{dt}>0 \)).
• Constant speed: The graph segment should be horizontal (slope \( = 0 \), as \( \frac{ds}{dt} = 0 \) when speed is constant).
• Slowing down: The graph segment should have a negative slope (since speed \( s \) decreases as time \( t \) increases, so \( \frac{ds}{dt}<0 \)).

Step3: Sketch the graph outline

• Start at the origin (or a low speed at \( t = 0 \)).
• Draw a line with a positive slope for the speeding - up phase.
• Then draw a horizontal line for the constant - speed phase (this line should be at the speed reached at the end of the speeding - up phase).
• Finally, draw a line with a negative slope (ending at speed \( = 0 \) or a lower speed) for the slowing - down phase. The x - axis is time (increasing to the right) and the y - axis is speed (increasing upwards).

Answer:

The qualitative graph will have three segments: a positively sloped segment (speeding up), a horizontal segment (constant speed), and a negatively sloped segment (slowing down), with the y - axis as speed and x - axis as time. (Note: Since it's a qualitative sketch, the exact values are not needed, just the shape based on the rate of change of speed with respect to time.)