Use the PhET simulation of the “Moving Man” in the textbook section on acceleration to simulate these motions. Use the PhET “Charts” to find the position, velocity and acceleration graphs and describe all of them with a sentence or two for each motion. (a) The Man moves slowly from the center to the right edge, then stops (b) The Man moves slowly from the center to the left edge, then reverses and goes back to the center where he stops. (c)The Man moves back and forth by 2m very slowly.
The correct answer and explanation is:
To analyze the motions described in your problem using the PhET “Moving Man” simulation and the associated charts for position, velocity, and acceleration, I’ll explain each motion scenario in detail.
(a) The Man moves slowly from the center to the right edge, then stops:
- Position Graph: The graph starts at the origin (center), then gradually increases in a slow, positive direction, showing a slow progression to the right. As the man stops, the graph flattens, indicating no movement at the end.
- Velocity Graph: The velocity starts positive, but the magnitude decreases steadily as the man slows down. Eventually, the velocity reaches zero as he comes to a stop at the right edge.
- Acceleration Graph: The acceleration is negative throughout the motion. Initially, it is constant, as the man decelerates uniformly, leading to a zero acceleration once he stops.
Explanation: In this scenario, the man starts moving slowly to the right, gradually reducing speed until he stops. The position graph reflects this gradual movement, while the velocity graph shows a decreasing speed (with zero velocity at the stop). The negative acceleration reflects the constant deceleration as the man slows down and eventually halts.
(b) The Man moves slowly from the center to the left edge, then reverses and goes back to the center where he stops:
- Position Graph: The graph starts at the center (origin) and increases slowly to the left. After reaching the left edge, the position graph turns back towards the center, indicating the reverse motion. The graph flattens when he reaches the center again and stops.
- Velocity Graph: The velocity is positive while the man moves to the left edge, then turns negative as he reverses direction towards the center. The velocity slowly decreases in magnitude as he decelerates and comes to a stop at the center.
- Acceleration Graph: Similar to the first motion, the acceleration is negative while the man decelerates. It is positive when the man reverses direction, as he accelerates back toward the center.
Explanation: This motion involves the man moving to the left and then reversing direction to return to the starting point. The position graph demonstrates this back-and-forth motion, while the velocity graph shows a transition from positive to negative values. The acceleration is negative while decelerating and positive when the man speeds up in the reverse direction.
(c) The Man moves back and forth by 2m very slowly:
- Position Graph: The graph shows a sinusoidal (oscillatory) pattern as the man moves back and forth between the two positions. The man moves slowly back and forth, creating a periodic fluctuation in position.
- Velocity Graph: The velocity graph oscillates similarly to the position graph but shifted to show the rate of movement at any point. The velocity will be highest when crossing the center and lowest at the maximum displacement.
- Acceleration Graph: The acceleration graph mirrors the velocity graph in its oscillatory nature, showing positive and negative values depending on the direction of motion. It will be zero when the man passes the center and reach maximum (negative or positive) at the edges of his movement.
Explanation: In this scenario, the man moves slowly back and forth by a small distance, creating an oscillatory motion. The position graph shows the repeated displacement, while the velocity graph reflects the changes in speed as the man changes direction. The acceleration graph follows suit, reflecting the changes in acceleration as the man speeds up and slows down during his motion.
Overall, these motions demonstrate the relationships between position, velocity, and acceleration in uniform and oscillatory motions, showcasing how each graph describes a distinct aspect of the motion.