The First Equation of Motion (v = u + at)
Simple Explanation
The first equation of motion, v = u + at, lets you find an object's final velocity (v) if you know its initial velocity (u), its acceleration (a), and the time (t) it accelerated for — without needing a graph.
Why Do We Need It?
This equation (and the three that follow it) let you solve motion problems directly with algebra, for any object moving with constant acceleration.
Formula
Equation of Motion: v = u + at
v = u + at
Final velocity from initial velocity, acceleration, and time.
- v
- — final velocity (m/s)
- u
- — initial velocity (m/s)
- a
- — acceleration (m/s²)
- t
- — time (s)
When to use it: Whenever you know initial velocity, acceleration and time, and need the final velocity.
Worked Example
Find a car's final velocity
A car starts at 5 m/s and accelerates at 3 m/s² for 4 s. Find its final velocity.
Why Does This Work?
Acceleration is defined as the change in velocity per second, so multiplying it by the time gives the total change in velocity over that time — adding that change to the starting velocity gives the final velocity.
Real-Life Example
Predicting a train's speed
A train accelerates steadily leaving a station.
Knowing its starting speed, acceleration, and how long it accelerates for lets engineers predict its speed at any later moment using this exact equation.
Practice
An object starts at 0 m/s and accelerates at 5 m/s² for 6 s. What is its final velocity?
EasyCommon mistake
Forgetting that u is the INITIAL velocity, not zero by default — u is only zero if the object starts from rest.
Quick Review
- v = u + at
- v = final velocity, u = initial velocity, a = acceleration, t = time.
- Only valid for constant (uniform) acceleration.