12. The area under the velocity vs time graph is supposed to be equal to the distance traveled along a straight line. Displacement = final position - initial position Distance: the distance traveled along the actual path. Since the average velocity = displacement (distance traveled along a straight line) / given time interval v = d/t d = vt Set the position of the man at -10.0 m, the velocity equal to 5 m's and the acceleration to 0.0. Run the simulation until the Moving Man hits the wall. What is the area under the velocity curve when the man reaches the +10 m mark? (You want velocity curve and the horizontal time axis. Realizing what kind of shape it is may help you calculate the area). Insert below a screen shot of the simulation for above description and your worksheet which shows how you obtain final answer for each question 39 seconds

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## Understanding Velocity-Time Graphs

### Overview

The area under the velocity vs time graph represents the distance traveled along a straight line. Here's how key concepts relate:

- **Displacement**: Final position minus initial position.
- **Distance**: The actual path traveled.

**Formula:**
- Average velocity = (displacement along a straight line) / (given time interval), or \( v = \frac{d}{t} \) and \( d = vt \).

### Simulation Instructions

Set the initial position to \(-10 \, \text{m}\), velocity to \(5 \, \text{m/s}\), and acceleration to \(0.0\). Run the simulation until the object hits the wall. Calculate the area under the velocity curve when the object reaches the \(+10 \, \text{m}\) mark. This involves calculating the area between the velocity curve and the horizontal time axis.

### Simulation Diagram Description

The diagram displays a simulation with time on the \(x\)-axis and velocity on the \(y\)-axis. The graph shows a horizontal line indicating constant velocity. The objective is to determine the distance by calculating the area under this line.

### Questions

a. What was the distance covered? _______ m

b. What is the area under the velocity curve? _______ m

c. What was the displacement of the man? _______ m

d. What was the speed of the man? _______ m/s  
(Remember speed = distance traveled / given time interval)

e. What was the velocity? _______ m/s and direction (if any) _______  
(Remember velocity = displacement / given time interval)
Transcribed Image Text:## Understanding Velocity-Time Graphs ### Overview The area under the velocity vs time graph represents the distance traveled along a straight line. Here's how key concepts relate: - **Displacement**: Final position minus initial position. - **Distance**: The actual path traveled. **Formula:** - Average velocity = (displacement along a straight line) / (given time interval), or \( v = \frac{d}{t} \) and \( d = vt \). ### Simulation Instructions Set the initial position to \(-10 \, \text{m}\), velocity to \(5 \, \text{m/s}\), and acceleration to \(0.0\). Run the simulation until the object hits the wall. Calculate the area under the velocity curve when the object reaches the \(+10 \, \text{m}\) mark. This involves calculating the area between the velocity curve and the horizontal time axis. ### Simulation Diagram Description The diagram displays a simulation with time on the \(x\)-axis and velocity on the \(y\)-axis. The graph shows a horizontal line indicating constant velocity. The objective is to determine the distance by calculating the area under this line. ### Questions a. What was the distance covered? _______ m b. What is the area under the velocity curve? _______ m c. What was the displacement of the man? _______ m d. What was the speed of the man? _______ m/s (Remember speed = distance traveled / given time interval) e. What was the velocity? _______ m/s and direction (if any) _______ (Remember velocity = displacement / given time interval)
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