1. Displacement (Δx):
* Δx = v₀t + (1/2)at²
* Δx = displacement
* v₀ = initial velocity
* t = time
* a = acceleration
2. Final velocity (v):
* v = v₀ + at
* v = final velocity
3. Relationship between velocity, displacement, and acceleration:
* v² = v₀² + 2aΔx
4. Average velocity:
* vₐ = (v₀ + v) / 2
Explanation:
* Displacement is the change in position of an object. It's a vector quantity, meaning it has both magnitude (how far the object moved) and direction.
* Velocity is the rate of change of displacement. It's also a vector quantity, indicating both speed and direction.
* Acceleration is the rate of change of velocity. It's also a vector quantity.
Important Notes:
* These formulas assume constant acceleration. If acceleration is not constant, you'll need to use calculus or other more advanced methods.
* Make sure to use consistent units for all quantities (e.g., meters for displacement, seconds for time, meters per second for velocity, and meters per second squared for acceleration).
Example:
Let's say a car starts from rest (v₀ = 0 m/s) and accelerates at a rate of 2 m/s² for 5 seconds. What is its final velocity?
* Using the formula v = v₀ + at, we can plug in the values:
* v = 0 + (2 m/s²)(5 s)
* v = 10 m/s
Therefore, the car's final velocity is 10 meters per second.
