Here's a breakdown of the equations, the variables, and some key points:
Variables:
* s: displacement (distance traveled)
* u: initial velocity
* v: final velocity
* a: acceleration
* t: time
The Equations:
1. v = u + at: This equation relates final velocity (v) to initial velocity (u), acceleration (a), and time (t). It tells us how the velocity changes over time.
2. s = ut + 1/2at²: This equation relates displacement (s) to initial velocity (u), acceleration (a), and time (t). It describes the distance traveled during uniformly accelerated motion.
3. v² = u² + 2as: This equation relates final velocity (v) to initial velocity (u), acceleration (a), and displacement (s). It directly relates the change in velocity to the distance traveled.
4. s = (u+v)/2 * t: This equation relates displacement (s) to initial velocity (u), final velocity (v), and time (t). It describes the average velocity over time.
Key Points:
* These equations only work for uniform acceleration. That means the acceleration must be constant over the entire time period considered.
* Direction matters. Remember to consider the signs of velocity and acceleration based on the chosen coordinate system. For example, if upward is positive, downward acceleration due to gravity would be negative.
* Choosing the right equation. You'll need to select the equation that has the variables you know and the variable you want to find.
Example:
A car accelerates from rest (u = 0 m/s) at a constant rate of 2 m/s² for 5 seconds.
* Find the final velocity (v): Use the equation v = u + at.
v = 0 + (2)(5) = 10 m/s.
* Find the distance traveled (s): Use the equation s = ut + 1/2at².
s = (0)(5) + 1/2(2)(5)² = 25 m.
Important Note: These equations assume the motion is in a straight line. For motion in two or three dimensions, you'll need to use vector equations and consider both the magnitude and direction of the quantities.
