CalculateY
Quick Answer
An object accelerating from 0 m/s to 20 m/s in 5 seconds has an acceleration of (20 - 0) / 5 = 4.0 m/s^2.
Common Examples
| Input | Result |
|---|---|
| v1 = 0, v2 = 20 m/s, t = 5 s | a = 4.00 m/s^2 |
| v1 = 0, a = 9.8 m/s^2, t = 3 s | v2 = 29.40 m/s |
| v1 = 10, v2 = 30 m/s, a = 5 m/s^2 | t = 4.00 s |
| v2 = 25 m/s, a = 2.5 m/s^2, t = 4 s | v1 = 15.00 m/s |
| v1 = 60, v2 = 0 m/s, t = 10 s | a = -6.00 m/s^2 (deceleration) |
How It Works
This calculator uses the fundamental kinematic equation for constant (uniform) acceleration:
a = (v₂ - v₁) / t
Where:
- a = acceleration in meters per second squared (m/s^2)
- v₁ = initial velocity in meters per second (m/s)
- v₂ = final velocity in meters per second (m/s)
- t = time in seconds (s)
This equation can be rearranged to solve for any of the four variables:
- Acceleration: a = (v₂ - v₁) / t
- Final velocity: v₂ = v₁ + a x t
- Time: t = (v₂ - v₁) / a
- Initial velocity: v₁ = v₂ - a x t
Positive vs. Negative Acceleration
A positive acceleration means the object is speeding up in the positive direction. A negative acceleration (sometimes called deceleration or retardation) means the object is slowing down or accelerating in the negative direction. For example, a car braking from 60 m/s to 0 m/s in 10 seconds has an acceleration of -6.0 m/s^2.
Constant Acceleration Assumption
This formula assumes constant (uniform) acceleration over the time interval. It does not apply to situations where acceleration changes over time, such as a rocket with increasing thrust or a car with varying braking force. For non-uniform acceleration, calculus-based methods are required.
Common Acceleration Values
The acceleration due to gravity near Earth’s surface is approximately 9.8 m/s^2 (often rounded to 9.81 or 10 m/s^2 for quick calculations). A car accelerating from 0 to 100 km/h in 8 seconds has an average acceleration of about 3.47 m/s^2.
Worked Example
A car starts from rest (v₁ = 0 m/s) and reaches a speed of 20 m/s in 5 seconds. The acceleration is a = (20 - 0) / 5 = 20 / 5 = 4.0 m/s^2. If that same car continued accelerating at 4.0 m/s^2 for another 3 seconds, its final velocity would be v₂ = 20 + 4.0 x 3 = 32 m/s. To find how long it takes to go from 20 m/s to 50 m/s at 4.0 m/s^2: t = (50 - 20) / 4.0 = 30 / 4.0 = 7.5 seconds.