Acceleration Calculator
Calculate acceleration, velocity, time, or distance using the kinematic equations. Convert between metric and imperial units.
Input Values
Unit System:
Solve For:
Acceleration
4.0000 m/s²
G-force: 0.408g
At This Acceleration:
0-60 mph time
24.14s
0-100 km/h time
25.00s
Formulas Used:
a = (v - v₀) / t
d = v₀t + ½at²
v² = v₀² + 2ad
Common Accelerations
Human walking
0.5 m/s²
Car (normal)
2-4 m/s²
Sports car
5-8 m/s²
Gravity (Earth)
9.81 m/s²
Fighter jet
30-90 m/s²
Space shuttle
29 m/s²
Understanding Acceleration
Acceleration is the rate of change of velocity. It tells us how quickly an object is speeding up or slowing down. A positive acceleration means the object is speeding up, while a negative acceleration (deceleration) means it's slowing down. The SI unit is meters per second squared (m/s²).
What is Acceleration?
Acceleration is the rate of change of velocity with respect to time. It's a vector quantity, meaning it has both magnitude and direction, and is fundamental to understanding motion in physics.
| Concept | Symbol | SI Unit | Description |
|---|---|---|---|
| Acceleration | a | m/s² | Rate of velocity change |
| Velocity | v | m/s | Rate of position change |
| Time | t | s | Duration of change |
| Displacement | Δx | m | Change in position |
Basic Acceleration Formula
Where:
- a= Acceleration (m/s²)
- v= Final velocity (m/s)
- v₀= Initial velocity (m/s)
- t= Time elapsed (s)
Types of Acceleration
Acceleration can take various forms depending on how velocity changes:
| Type | Description | Example |
|---|---|---|
| Positive Acceleration | Velocity increasing in direction of motion | Car speeding up |
| Negative Acceleration (Deceleration) | Velocity decreasing | Car braking |
| Centripetal Acceleration | Direction change at constant speed | Car turning a corner |
| Uniform Acceleration | Constant rate of change | Free fall (ignoring air) |
| Non-uniform Acceleration | Varying rate of change | Rocket launch |
| Angular Acceleration | Rate of change of angular velocity | Spinning wheel speeding up |
Kinematic Equations for Constant Acceleration
When acceleration is constant, these four kinematic equations describe the motion:
| Equation | Variables | Use When |
|---|---|---|
| v = v₀ + at | v, v₀, a, t | No displacement needed |
| x = v₀t + ½at² | x, v₀, a, t | No final velocity needed |
| v² = v₀² + 2ax | v, v₀, a, x | No time needed |
| x = ½(v + v₀)t | x, v, v₀, t | No acceleration needed |
Strategy: Identify three known quantities and one unknown, then select the equation containing exactly those four variables.
Kinematic Equations
Where:
- x= Displacement (m)
- v₀= Initial velocity (m/s)
- v= Final velocity (m/s)
- a= Acceleration (m/s²)
- t= Time (s)
Gravitational Acceleration
Gravitational acceleration (g) is the acceleration caused by gravity, varying by location:
| Location | g Value | Notes |
|---|---|---|
| Earth (sea level) | 9.81 m/s² | Standard value (often rounded to 10) |
| Earth (equator) | 9.78 m/s² | Reduced by Earth's rotation |
| Earth (poles) | 9.83 m/s² | No centrifugal effect |
| Moon | 1.62 m/s² | About 1/6 of Earth's |
| Mars | 3.71 m/s² | About 38% of Earth's |
| Jupiter | 24.79 m/s² | About 2.5× Earth's |
Free Fall Equations
Where:
- g= Gravitational acceleration (9.81 m/s² on Earth)
- y= Vertical displacement (m)
- v₀= Initial velocity (m/s)
Centripetal Acceleration
Centripetal acceleration occurs when an object moves in a circular path, constantly changing direction even if speed remains constant.
| Quantity | Formula | Unit |
|---|---|---|
| Centripetal acceleration | aᴄ = v²/r = ω²r | m/s² |
| Centripetal force | Fᴄ = mv²/r = mω²r | N |
| Angular velocity | ω = v/r = 2πf | rad/s |
| Period | T = 2πr/v = 1/f | s |
Direction: Centripetal acceleration always points toward the center of the circular path, perpendicular to velocity.
Centripetal Acceleration
Where:
- aᴄ= Centripetal acceleration (m/s²)
- v= Tangential velocity (m/s)
- r= Radius of circular path (m)
- ω= Angular velocity (rad/s)
Acceleration and Newton's Second Law
Newton's Second Law directly relates acceleration to force and mass:
| Relationship | Implication | Example |
|---|---|---|
| F = ma | Force produces acceleration | Pushing a cart |
| a = F/m | More mass = less acceleration | Loaded vs empty truck |
| ΣF = ma | Net force determines acceleration | Tug of war |
Key insight: An object accelerates only when a net force acts on it. No net force means constant velocity (including zero).
Newton's Second Law
Where:
- F= Force (Newtons, N)
- m= Mass (kg)
- a= Acceleration (m/s²)
Real-World Applications
Acceleration calculations are essential in many fields:
| Application | Typical Values | Considerations |
|---|---|---|
| Vehicle performance | 0-60 mph in 3-10 s | Marketing specs, 0-100 km/h |
| Roller coasters | Up to 6g | Human tolerance limits |
| Aircraft takeoff | 0.3-0.5g | Runway length calculations |
| Braking systems | 0.8-1.0g maximum | Tire friction limits |
| Elevators | 1-1.5 m/s² | Comfort considerations |
| Spacecraft launch | 3-4g sustained | Astronaut training required |
Worked Examples
Car Acceleration from Rest
Problem:
A sports car accelerates from 0 to 100 km/h in 5 seconds. Calculate the acceleration.
Solution Steps:
- 1Convert units: 100 km/h = 100 × (1000/3600) = 27.78 m/s
- 2Apply formula: a = (v - v₀) / t
- 3Substitute: a = (27.78 - 0) / 5
- 4Calculate: a = 5.56 m/s²
- 5Express in g: 5.56 / 9.81 = 0.57g
Result:
Acceleration = 5.56 m/s² (0.57g)
Braking Distance
Problem:
A car traveling at 30 m/s brakes with deceleration of 8 m/s². Find the stopping distance.
Solution Steps:
- 1Given: v₀ = 30 m/s, v = 0, a = -8 m/s²
- 2Use: v² = v₀² + 2ax
- 3Solve for x: 0 = 30² + 2(-8)x
- 40 = 900 - 16x
- 5x = 900/16 = 56.25 m
Result:
Stopping distance = 56.25 meters
Centripetal Acceleration
Problem:
A car takes a curve of radius 50 m at 20 m/s. What is the centripetal acceleration?
Solution Steps:
- 1Use formula: aᴄ = v²/r
- 2Substitute: aᴄ = 20²/50
- 3Calculate: aᴄ = 400/50 = 8 m/s²
- 4Express in g: 8/9.81 = 0.82g
Result:
Centripetal acceleration = 8 m/s² (0.82g)
Tips & Best Practices
- ✓Always check units: acceleration should be in m/s², not m/s or m/s³
- ✓Draw a diagram with arrows showing positive direction before solving
- ✓When using kinematic equations, be consistent with signs for direction
- ✓For vertical motion, decide if up or down is positive and stick with it
- ✓Remember: zero velocity doesn't mean zero acceleration (ball at top of throw)
- ✓Convert km/h to m/s by multiplying by (1000/3600) = 0.278
- ✓Use v² = v₀² + 2ax when time isn't given or needed
Frequently Asked Questions
Sources & References
Last updated: 2026-01-22