Math Problem Statement
Solution
To calculate the average velocity for each interval, we use the formula for average velocity:
where:
- is the change in position (displacement),
- is the change in time.
Let's analyze each time interval using the graph you've provided:
1. Between 0 and 2 seconds:
From the graph:
- At , the position is meters.
- At , the position is meters.
So:
2. Between 2 and 3 seconds:
From the graph:
- At , the position is meters.
- At , the position is still meters (no change in position).
So:
3. Between 3 and 5 seconds:
From the graph:
- At , the position is meters.
- At , the position is meters.
So:
4. Between 5 and 8 seconds:
From the graph:
- At , the position is meters.
- At , the position is meters.
So:
Part b: Average velocity for the overall motion (from 0 to 8 seconds):
From the graph:
- The total displacement from to is:
- At , position is meters.
- At , position is meters.
So the total displacement is and the total time is .
Summary:
- Between 0 and 2 s:
- Between 2 and 3 s:
- Between 3 and 5 s:
- Between 5 and 8 s:
- Overall average velocity:
Do you want further clarification or details on these calculations?
Here are five related questions for deeper understanding:
- What would happen if the object had moved backward in any interval?
- How does the slope of the graph relate to the velocity in each interval?
- What is the difference between instantaneous velocity and average velocity?
- How would the graph look if the object moved with constant velocity?
- Can velocity be negative? How would that appear on the graph?
Tip: Average velocity depends on the total displacement, not the total distance traveled!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Kinematics
Average Velocity
Position-Time Graph
Formulas
v_avg = Δx / Δt
Theorems
-
Suitable Grade Level
Grades 9-12
Related Recommendation
Calculating Average Velocity from a Position-Time Graph
Calculate Average Velocity Problems from a Position-Time Graph
Calculate the Average Velocity from 0 to 2 Seconds Using a Position-Time Graph
Kinematics Problem: Average Velocity and Acceleration of a Particle
Position-Time Graph Analysis: Average and Instantaneous Velocity