https://file.aiquickdraw.com/mathbot/file/1724765444921m4yz6p5t.jpg

solve for the acceleration at 5.5 seconds

To solve for the acceleration at 5.5 seconds, we'll analyze the velocity-time graph provided in the image. Acceleration is defined as the rate of change of velocity with respect to time, which can be found by calculating the slope of the velocity-time graph.

### Steps to solve:
1. **Identify the interval**: Determine the time interval within which 5.5 seconds falls and observe the behavior of the velocity graph in that region.

2. **Calculate the slope**: The acceleration is the slope of the velocity-time graph. To find the slope, we'll use the formula:

   \[
   \text{Slope (acceleration)} = \frac{\Delta v}{\Delta t}
   \]

   where \(\Delta v\) is the change in velocity and \(\Delta t\) is the change in time.

### Analysis:
- At \( t = 5.5 \) seconds, the graph is on a downward sloping line segment.
- From the graph:
  - At \( t = 5 \) seconds, \( v = 0 \, \text{m/s} \).
  - At \( t = 6 \) seconds, \( v = -4 \, \text{m/s} \).

### Calculation:
- The change in velocity (\(\Delta v\)) from \( t = 5 \) seconds to \( t = 6 \) seconds is:
  \[
  \Delta v = -4 - 0 = -4 \, \text{m/s}
  \]
- The change in time (\(\Delta t\)) is:
  \[
  \Delta t = 6 - 5 = 1 \, \text{second}
  \]
- Therefore, the acceleration is:
  \[
  \text{Acceleration} = \frac{-4 \, \text{m/s}}{1 \, \text{s}} = -4 \, \text{m/s}^2
  \]

### Conclusion:
The acceleration at 5.5 seconds is \(-4 \, \text{m/s}^2\).

Would you like more details on this solution, or do you have any other questions?

Here are some related questions you might find helpful:
1. What is the acceleration between 0 to 2 seconds?
2. What is the total displacement of the object by the end of the 6-second interval?
3. How would you calculate the average velocity of the object over the entire 6-second period?
4. What does the area under the velocity-time graph represent?
5. Can you determine the direction of the object’s movement based on the velocity-time graph?

**Tip:** The slope of a velocity-time graph gives you the acceleration, while the area under the curve gives you the displacement.

Learn how to calculate acceleration at 5.5 seconds from a velocity-time graph with a step-by-step solution. Understand the concept of acceleration, slope calculation, and interpretation of velocity-time graphs. Suitable for high school students studying physics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation