The linear motion equations, also known as kinematic equations, describe the motion of an object moving in a straight line with constant acceleration. These fundamental equations relate displacement, initial velocity, final velocity, acceleration, and time.
Key Kinematic Equations
There are four primary kinematic equations used to solve problems involving linear motion under constant acceleration. These equations are derived from the definitions of velocity and acceleration.
Here are the four kinematic equations:
| Equation | Description | Variables Included | Reference Source |
|---|---|---|---|
1. vf = vi + a*t |
Final velocity equals initial velocity plus acceleration times time. | vf, vi, a, t |
Included in reference |
2. d = vi*t + 0.5*a*t^2 |
Displacement equals initial velocity times time plus one-half acceleration times time squared. | d, vi, a, t |
Included in reference |
3. vf^2 = vi^2 + 2*a*d |
Final velocity squared equals initial velocity squared plus two times acceleration times displacement. | vf, vi, a, d |
Included in reference (uses x instead of d) |
4. d = 0.5*(vi + vf)*t |
Displacement equals the average velocity (initial plus final divided by two) times time. | d, vi, vf, t |
Not explicitly listed in this reference excerpt |
Note: The provided reference explicitly lists the first three equations.
Understanding the Variables
To effectively use these equations, it's important to understand what each variable represents:
vi: Initial velocity (the object's velocity at the start of the motion).vf: Final velocity (the object's velocity at the end of the motion).a: Constant acceleration (the rate at which the object's velocity changes). This must be constant for these equations to apply.t: Time interval (the duration of the motion).d: Displacement (the change in the object's position). In the third equation listed in the reference, this is represented byx.
When to Use These Equations
These kinematic equations are applicable only when:
- The motion is along a straight line (linear).
- The acceleration is constant.
They are powerful tools for analyzing motion in various scenarios, from calculating how far a car travels while accelerating to determining the speed of a falling object (assuming negligible air resistance, which results in constant acceleration due to gravity).
