Here are the most common equations of motion for linear motion with constant acceleration:
1. Velocity-Time Equation:
* v = u + at
* v: final velocity
* u: initial velocity
* a: acceleration
* t: time
2. Displacement-Time Equation:
* s = ut + (1/2)at²
* s: displacement
* u: initial velocity
* a: acceleration
* t: time
3. Velocity-Displacement Equation:
* v² = u² + 2as
* v: final velocity
* u: initial velocity
* a: acceleration
* s: displacement
Key Points:
* Constant Acceleration: These equations are valid only for objects moving with a constant acceleration.
* Linear Motion: They describe motion in a straight line.
* Assumptions: These equations assume no air resistance or other external forces acting on the object.
Example:
Let's say a car starts from rest (u = 0 m/s) and accelerates at a constant rate of 2 m/s² for 5 seconds. Using the equations of motion, we can find:
* Final velocity (v): v = u + at = 0 + (2)(5) = 10 m/s
* Displacement (s): s = ut + (1/2)at² = 0 + (1/2)(2)(5)² = 25 meters
Beyond Linear Motion:
Equations of motion can be extended to describe more complex scenarios involving rotational motion, projectile motion, and other types of motion. However, the core principles remain the same: they provide mathematical relationships between the position, velocity, and acceleration of an object over time.
