The equation you're referring to is:

\[
d = -100 + vt + \frac{1}{2}at^2
\]

This equation is a kinematic equation used to describe the displacement \(d\) of an object under constant acceleration \(a\), with initial velocity \(v\) and time \(t\). Here’s a breakdown of each term:

- \(-100\): This could represent an initial displacement or position, meaning the object starts 100 units behind a reference point.
- \(vt\): This is the displacement due to the initial velocity \(v\) over time \(t\).
- \(\frac{1}{2}at^2\): This term accounts for the displacement due to constant acceleration \(a\) over time \(t\).

### Explanation of the Equation:
- **\(d\)**: Total displacement.
- **\(-100\)**: Initial position, suggesting the object starts from a position 100 units behind the origin or reference point.
- **\(vt\)**: The displacement due to the object's initial velocity over time \(t\).
- **\(\frac{1}{2}at^2\)**: The displacement caused by acceleration over time \(t\).

This equation combines the effects of initial velocity and constant acceleration on the object's displacement from an initial position.

Would you like to solve a problem using this equation, or do you have other questions related to it?

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Here are 8 follow-up questions that could expand on this information:

1. How would you find the time \(t\) when the object reaches a specific displacement \(d\)?
2. What does it mean physically if the displacement \(d\) is negative?
3. How does changing the initial velocity \(v\) affect the overall displacement \(d\)?
4. Can you derive this equation from the basic laws of motion?
5. What are the conditions under which this equation is valid?
6. How does this equation change if the acceleration \(a\) is zero?
7. What is the significance of the term \(\frac{1}{2}at^2\) in this equation?
8. How would you plot \(d\) versus \(t\) for different values of \(a\) and \(v\)?

**Tip:** When solving kinematic problems, make sure to clearly define your coordinate system and pay attention to the signs (positive or negative) associated with displacement, velocity, and acceleration.

Explore the kinematic equation d = -100 + vt + 1/2at^2 used to describe displacement under constant acceleration. Learn how each term contributes to the total displacement, including initial position, velocity, and acceleration effects. Suitable for high school students studying physics and motion equations.

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