Kinematic Equations
The four kinematic equations describe motion with constant acceleration.
Master velocity, displacement, and time calculations with step-by-step examples.
The Formulas
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
These four equations describe the motion of an object under constant acceleration. Each equation connects different combinations of the five variables: u, v, a, s, and t.
Variables
| Symbol | Meaning |
|---|---|
| u | Initial velocity (m/s) |
| v | Final velocity (m/s) |
| a | Acceleration (m/s²) |
| s | Displacement (m) |
| t | Time (s) |
Example 1
A car starts from rest and accelerates at 4 m/s² for 8 seconds. How far does it travel?
Known values: u = 0 m/s, a = 4 m/s², t = 8 s
Use: s = ut + ½at²
s = (0)(8) + ½(4)(8²) = 0 + ½(4)(64)
s = 128 m
Example 2
A bicycle moving at 15 m/s brakes to a stop over 45 m. What is the deceleration?
Known values: u = 15 m/s, v = 0 m/s, s = 45 m
Use: v² = u² + 2as
0 = 15² + 2a(45)
0 = 225 + 90a
a = -225 / 90
a = -2.5 m/s² (the negative sign indicates deceleration)
When to Use It
Use the kinematic equations for any problem involving straight-line motion with constant acceleration.
- Objects falling under gravity (a = 9.81 m/s²)
- Vehicles accelerating or braking
- Projectile motion (vertical component)
- Choose the equation that contains the three known variables and the one unknown