How fast is the speed changing?
Find acceleration two ways: from a change in velocity over time, or from a force pushing on a mass. See the answer in m/s squared, ft/s squared and g-force, plus the distance covered and the time to reach 60 mph.
The motion
For the velocity method this is how long the change takes. For the force method it is how long the force acts, used to project speed and distance from rest.
What this acceleration means
Velocity building over time
Speed versus time, the slope is the acceleration
Milestones
Speed and distance, second by second
Velocity reached and ground covered at each moment, starting from the current velocity at the given acceleration.
| Time | Velocity (m/s) | Velocity (mph) | Distance (m) | Distance (ft) |
|---|
Acceleration, explained
The Acceleration Formula
Acceleration equals the change in velocity divided by the time over which the change occurred: a = (v_final - v_initial) / t. The SI unit is meters per second squared (m/s²). Earth's gravity is approximately 9.81 m/s², every second of free fall adds 9.81 m/s to your downward velocity.
Positive vs Negative Acceleration
Positive acceleration means your final velocity is greater than your initial velocity. Negative acceleration (deceleration) means you are slowing down. Note that 'negative' is purely a sign relative to your chosen direction, a car braking from 30 m/s to 0 m/s in 5 seconds has an acceleration of -6 m/s², which is still significant.
Real-World Acceleration Values
Gravity: 9.81 m/s². Sports car 0-60 mph in 4 seconds: 6.7 m/s². Commercial airliner takeoff: 1.5-3 m/s². Drag racing: 30-60 m/s². Roller coaster peak: 30-50 m/s². Concussion risk in vehicle crash: above 60 m/s² (6g). Astronaut training: up to 90 m/s² (9g) for short bursts.
Using Acceleration to Find Other Quantities
If you know acceleration and time, you can compute final velocity: v_f = v_i + a*t. Knowing acceleration and initial velocity, you can find distance traveled: d = v_i*t + 0.5*a*t². Use this calculator for the basic case, then plug into kinematic equations for deeper analysis.
Common questions
What does negative acceleration mean?
It means the object is decelerating, final velocity is less than initial velocity. The object is still moving (or stationary at the end), just slowing down or moving in the opposite direction.
Why is gravity 9.81 m/s²?
That is the standard average value of Earth's gravitational acceleration at sea level. It varies slightly with latitude (9.78 at equator, 9.83 at poles) and altitude (slightly less at higher altitudes).
What's the unit 'g' in g-forces?
1 g equals Earth gravity (9.81 m/s²). A 4g acceleration is 4 × 9.81 = 39.24 m/s². Humans can tolerate ~5g sustained and ~10g for brief moments without serious injury.
How is this different from velocity?
Velocity is how fast you are moving. Acceleration is how quickly your velocity is changing. A car at constant 60 mph has high velocity but zero acceleration.
Can acceleration be zero with motion?
Yes, an object moving at constant velocity has zero acceleration. Acceleration only measures the CHANGE in velocity, not motion itself.
Estimates assume constant acceleration and ignore air resistance, friction and other real-world losses. Use for learning and planning, verify with measured data for engineering work.