Kinematics: Velocity
Final velocity under constant acceleration.
Formula
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Example
Starting at 5 m/s and accelerating 2 m/s² for 3 s: v = 5 + 2·3 = 11 m/s.
How it works
This formula tells you how an object's velocity changes when it speeds up or slows down at a constant rate. It comes from the definition of acceleration: acceleration is the change in velocity per unit time, so rearranging gives the final velocity as initial velocity plus acceleration multiplied by time. It only works when the acceleration stays constant throughout the time interval.
When to use it
Use this for straight-line motion with constant acceleration, such as a car accelerating steadily, an object falling freely near Earth, or a cyclist slowing at a constant rate. It is useful whenever you know the starting speed, the acceleration, and how long the motion lasts.
Worked example, step by step
A train is moving at 12 m/s and accelerates at 1.5 m/s² for 4 s. Step 1: Write the formula: v = u + at Step 2: Substitute the values: v = 12 + (1.5)(4) Step 3: Calculate: v = 12 + 6 Step 4: Final answer: v = 18 m/s
Common mistakes to avoid
- Using the formula when acceleration is not constant
- Forgetting that deceleration is a negative acceleration
- Mixing up initial velocity u with final velocity v
Did You Know?
These kinematic equations assume constant acceleration — exactly the case for objects in free fall.
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