Mechanics
Kinematic Equation 4
Displacement using average velocity.
Variables
xm
Final position
Position at time t
x₀m
Initial position
Initial position
v₀m/s
Initial velocity
Initial velocity
vm/s
Final velocity
Final velocity
ts
Time
Elapsed time
Derivation
Average velocity = (v₀ + v)/2, so x - x₀ = v_avg × t.
Your notes
0/5000
Check value
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- x₀ = 2 m (Initial position)
- v₀ = 3 m/s (Initial velocity)
- v = 4 m/s (Final velocity)
- t = 5 s (Time)
Result: x = 19.5 m
Other mechanics formulas with the same quantities
- Free Fall (Kinematics) shares Initial velocity, Time
- Projectile Range (Kinematics) shares Initial velocity
- Projectile Maximum Height (Kinematics) shares Initial velocity
- Projectile Time of Flight (Kinematics) shares Initial velocity
Where this formula is listed
- Mechanics formulas, under Kinematics, alongside Velocity, Acceleration and Average Velocity.
- In the mechanics list it comes after Kinematic Equation 3 and before Free Fall.
- Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Kinematic Equation 4 formula?
Kinematic Equation 4 is written x = x₀ + (1/2)(v₀ + v)t. Displacement using average velocity. It belongs to Mechanics, under Kinematics.
What are the units in x = x₀ + (1/2)(v₀ + v)t?
In SI units, x is final position, measured in m; x₀ is initial position, measured in m; v₀ is initial velocity, measured in m/s; v is final velocity, measured in m/s; t is time, measured in s.
How is the Kinematic Equation 4 formula derived?
Average velocity = (v₀ + v)/2, so x - x₀ = v_avg × t. The result is x = x₀ + (1/2)(v₀ + v)t.