Question

speed of jogger on a track:
a jogger is running along a track. at the beginning, she walks at a constant speed to warm up, then she speeds up and runs at a constant speed for two laps. she speeds up for one lap, slows down, then walks one lap to cool down.
sketch a qualitative graph to represent the scenario.
(there is a coordinate system with speed on the horizontal axis and time on the vertical axis, and some blank lines below for sketching.)

Explanation:

Step1: Identify the phases

The jogger's motion has several phases: walking (constant speed) to warm up, speeding up and running at constant speed for two laps, speeding up for one lap, slowing down, and walking one lap to cool down.

Step2: Sketch the graph

• Warm - up (walking): A horizontal line (constant speed) starting from some initial speed (low) on the speed - time graph.
• Speeding up (first acceleration): A line with a positive slope (increasing speed) until she reaches the speed for the two - lap constant speed run.
• Constant speed (two laps): A horizontal line (constant speed) at the speed reached after the first acceleration.
• Speeding up (second acceleration): A line with a positive slope (increasing speed) from the previous constant speed.
• Slowing down: A line with a negative slope (decreasing speed) from the speed reached after the second acceleration.
• Cool - down (walking): A horizontal line (constant speed) at a low speed (similar to the warm - up speed) until the end of the motion.

We can represent this on a speed - time graph where the x - axis is time and the y - axis is speed. The key is to show the changes in speed over time with appropriate line segments (horizontal for constant speed, sloped for acceleration/deceleration).

Answer:

The graph will have the following segments (from left to right, as time increases):

1. A horizontal line (constant low speed) for the warm - up walking phase.
2. A line with a positive slope (speeding up) to reach the speed for the two - lap constant speed run.
3. A horizontal line (constant speed) for the two - lap running phase.
4. A line with a positive slope (speeding up) for the one - lap acceleration phase.
5. A line with a negative slope (slowing down) from the speed of the previous phase.
6. A horizontal line (constant low speed) for the cool - down walking phase.

(Note: Since it is a qualitative sketch, the exact values of speed and time are not needed, just the general shape of the graph showing the changes in speed over time as described above.)