Question

1. graphs a sprinter walks up to the starting blocks at a constant speed and positions herself for the start of the race. she waits until she hears the starting pistol go off and then accelerates rapidly until she attains a constant velocity. she maintains this velocity until she crosses the finish line, and then she slows to a walk, taking more time to slow down than she did to speed up at the beginning of the race. sketch a velocity - time and a position - time graph to represent her motion. draw them one above the other using the same time scale. indicate on your position - time graph where the starting blocks and finish line are.

Explanation:

Step1: Analyze the sprinter's motion phases for velocity - time graph

1. Walking to starting blocks: Constant speed, so velocity is non - zero and constant.
2. Waiting: Velocity is 0.
3. Accelerating: Positive acceleration, so velocity increases linearly.
4. Constant velocity phase: Velocity is constant and non - zero.
5. Slowing down: Negative acceleration, velocity decreases linearly over a longer time compared to acceleration phase.

Step2: Analyze the sprinter's motion phases for position - time graph

1. Walking to starting blocks: Position changes linearly with a non - zero slope (due to constant speed).
2. Waiting: Position is constant (slope = 0).
3. Accelerating: Position - time graph is a curve with increasing slope (due to increasing velocity).
4. Constant velocity phase: Position changes linearly with a constant non - zero slope.
5. Slowing down: Position - time graph is a curve with decreasing slope. Mark the starting position as the starting blocks and the final position as the finish line.

Answer:

For the velocity - time graph:

1. Start with a non - zero horizontal line for walking to starting blocks.
2. Then a horizontal line at \(v = 0\) for waiting.
3. Followed by an upward - sloping line for acceleration.
4. Then a horizontal line for constant velocity.
5. Finally, a downward - sloping line with a shallower slope than the acceleration line for slowing down.

For the position - time graph:

1. Start with a line with a non - zero slope for walking to starting blocks.
2. Then a horizontal line for waiting.
3. Followed by a curve with increasing slope for acceleration.
4. Then a line with a constant non - zero slope for constant velocity.
5. Finally, a curve with decreasing slope. Mark the starting and ending positions.