d = v₀t + (1/2)at²
Here's what each variable represents:
* d: Displacement (the change in position)
* v₀: Initial velocity (the velocity at the start of the time interval)
* t: Time (the duration of the motion)
* a: Acceleration (the rate of change of velocity)
Explanation:
This formula combines two fundamental concepts of motion:
1. Uniform Motion: The term v₀t represents the displacement that would occur if the object moved at a constant initial velocity for the entire time interval.
2. Acceleration: The term (1/2)at² accounts for the change in displacement due to the acceleration. The object's velocity changes over time, leading to an additional displacement beyond the initial velocity term.
Important Notes:
* This formula assumes constant acceleration. If the acceleration is not constant, you'll need more complex methods to calculate displacement.
* The formula is valid for both linear and vertical motion (assuming constant acceleration due to gravity).
* Make sure to use consistent units for all variables (e.g., meters for displacement, meters per second for velocity, meters per second squared for acceleration, and seconds for time).
