The equation you've provided is a standard kinematic equation in physics that describes the displacement \( s \) of an object under constant acceleration \( a \), with initial velocity \( v \), over a time \( t \).

The equation is:

\[
s = \frac{1}{2}at^2 + vt
\]

### Components:
- \( s \) = Displacement (how far the object has moved)
- \( a \) = Constant acceleration
- \( t \) = Time
- \( v \) = Initial velocity

### Explanation:
- The term \( \frac{1}{2}at^2 \) accounts for the displacement due to acceleration over time \( t \).
- The term \( vt \) accounts for the displacement due to the initial velocity \( v \) over time \( t \).

Together, these give the total displacement \( s \) after time \( t \).

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:

1. How can this equation be applied to determine the maximum height reached by an object thrown upwards?
2. What changes if the object starts from rest (i.e., \( v = 0 \))?
3. How can you derive this equation from the basic principles of motion?
4. What are the assumptions behind using this kinematic equation?
5. How does this equation change if the acceleration \( a \) is not constant?

**Tip:** Remember that this equation only applies under constant acceleration. If acceleration varies with time, a different approach is needed.

Explore the kinematic equation s = \frac{1}{2}at^2 + vt used in physics to calculate displacement under constant acceleration. Learn about its components including displacement, constant acceleration, time, and initial velocity. Suitable for students studying physics in Grades 11-12.

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