Earth gravity ≈ 9.81 m/s²
v = u + at; s = ut + ½at²The first kinematic equation gives final velocity from initial velocity, constant acceleration, and time. The second gives displacement under the same conditions. These hold for any straight-line motion with constant acceleration: free fall, braking cars, accelerating projectiles.
Enter initial velocity, acceleration, and time. Get final velocity and displacement.
Enter your initial velocity, acceleration, and elapsed time to get the final velocity and the distance traveled. The calculator uses the standard kinematic equations that apply to any straight-line motion with constant acceleration, from free fall to car braking.
Kinematics, the math of motion, starts with three quantities: velocity, acceleration, and time. Given any two, you can solve for almost any motion problem. This calculator handles the most common case: known initial velocity, constant acceleration, and known elapsed time.
Definition
The computation, step by step
- 1Enter the initial velocity (u). Use 0 if the object starts at rest.
- 2Enter the acceleration (a). Use 9.81 m/s² for objects in free fall on Earth.
- 3Enter the elapsed time (t).
- 4The calculator applies v = u + at for final velocity.
- 5It also computes displacement using s = ut + ½at².
Solved example
A worked solution
Example: Object dropped from rest for 3 seconds
- 1u = 0, a = 9.81 m/s², t = 3 s
- 2v = 0 + 9.81 × 3 = 29.43 m/s
- 3s = 0 + 0.5 × 9.81 × 9 = 44.1 m
Validity
Edge cases and pitfalls
- Using these equations with non-constant acceleration: These formulas only work when acceleration stays constant. If the force on the object changes during the motion, you need calculus or numerical integration.
- Mixing m/s with km/h: 60 km/h is 16.67 m/s, not 60 m/s. Always convert speeds to m/s before applying the equations.
- Forgetting that g acts downward: When an object is thrown upward, the initial velocity is positive but acceleration is negative (-9.81 m/s²) because gravity points down. Sign matters.
- Ignoring air resistance for fast or light objects: These equations assume no drag. For a feather, a parachute, or anything moving faster than 30 m/s, air resistance changes the answer significantly.
Adjacent topics
Related concepts
| Term | Definition |
|---|---|
| Velocity | Speed in a specific direction. Measured in meters per second (m/s) in SI. |
| Acceleration | The rate of change of velocity. Constant acceleration is required for these kinematic equations to apply. |
| Displacement | Net change in position. Distance traveled in a straight line. Different from total path length when motion changes direction. |
| g (gravitational acceleration) | 9.81 m/s² on Earth's surface. The acceleration of any freely falling object near Earth, ignoring air resistance. |
Applications
Where this calculation appears
- Physics homework: Solve standard kinematics problems for any combination of velocity, acceleration, and time.
- Free fall calculations: Estimate the velocity and distance of a falling object given drop time.
- Vehicle braking: Calculate stopping distance given initial speed and a negative acceleration.
- Projectile motion (vertical component): Find the vertical velocity and height of a projectile at any time.
Implementation notes
Pro tips
- Pick a positive direction and stick with it: Before doing the math, choose which direction is positive (usually up or forward). Apply that sign convention to velocity, acceleration, and displacement consistently.
- Use 10 m/s² for rough estimates: g is close enough to 10 m/s² for back-of-the-envelope work. After 5 seconds of falling you reach 50 m/s and 125 m.
- Verify with average velocity: For constant acceleration, average velocity equals (u + v) / 2. Multiply by time to cross-check displacement.
- Remember terminal velocity exists: Free fall predictions break down past terminal velocity. A human in a belly-down position reaches about 53 m/s (120 mph) terminal, not the 200+ m/s the equations predict after 20 seconds.
Common questions
Frequently asked questions
Quick reference
Final Velocity and Distance for Free Fall
Object dropped from rest, ignoring air resistance
| Time | Velocity | Distance fallen |
|---|---|---|
| 1 s | 9.81 m/s | 4.9 m |
| 2 s | 19.62 m/s | 19.6 m |
| 3 stypical | 29.43 m/s | 44.1 m |
| 5 s | 49.05 m/s | 122.6 m |
| 10 s | 98.1 m/s | 490.5 m |
For related calculations, try the Speed Calculator, Acceleration Calculator, or Kinetic Energy. Browse all Calculator Online calculators for the full catalog.
Methodology
This calculator uses the standard velocity calculator formula. Results match those from established financial, scientific, and health references.
Reviewed by
Calculator Online Editorial Team. All formulas verified against authoritative sources before publication.
Last updated
2026-05-24