Acceleration Calculator
Acceleration is the rate of change of velocity over time. This calculator computes acceleration given initial velocity, final velocity, and time elapsed. It also returns distance traveled under constant acceleration using kinematic equations.
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Formula
a = (v − u) / t
Acceleration (a) equals the change in velocity divided by time: a = (v − u) / t, where v is final velocity, u is initial velocity, and t is time. Distance under constant acceleration uses the kinematic equation: d = ut + ½at². G-force is acceleration divided by 9.81 m/s².
How to use the Acceleration Calculator
- 1
Enter your initial velocity
Value should be in m/s.
- 2
Enter your final velocity
Value should be in m/s.
- 3
Enter your time
Value should be in s.
- 4
Read your results instantly
Results update in real time as you type.
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What acceleration really means
Acceleration is any change in velocity — speeding up, slowing down, or changing direction. A car going from 0 to 100 km/h in 5 seconds accelerates at about 5.56 m/s². Braking from 100 km/h to 0 in 4 seconds produces a deceleration of about 6.94 m/s² (about 0.7g). Even a car rounding a curve at constant speed is accelerating, because its direction is changing.
The SI unit of acceleration is meters per second squared (m/s²). This means for every second that passes, velocity changes by that many m/s. At 5 m/s², an object at rest reaches 5 m/s after 1 second, 10 m/s after 2 seconds, and so on (assuming constant acceleration).
G-force and human tolerance
G-force measures acceleration relative to Earth's gravitational pull (9.81 m/s²). At rest, you experience 1g. A roller coaster might pull 3-5g in a tight corner. Fighter pilots can experience 9g briefly with a G-suit. Unconsciousness typically occurs around 4-6g sustained without a G-suit, as blood pools away from the brain.
Car crashes are often measured in g: a 30 mph frontal crash with a 0.1-second stop produces around 130g — far exceeding human survivability without airbags and crumple zones that extend the stopping time to 100+ milliseconds. Formula 1 drivers routinely survive 50g+ crashes because safety cells and HANS devices distribute forces over larger areas and longer times.
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Kinematic equations for constant acceleration
When acceleration is constant, four kinematic equations relate displacement (d), initial velocity (u), final velocity (v), acceleration (a), and time (t):
1. v = u + at 2. d = ut + ½at² 3. v² = u² + 2ad 4. d = (u + v)t / 2
These equations underpin much of introductory physics. They apply to free fall, projectile motion (vertical component), and any situation with uniform acceleration. For non-constant acceleration, calculus is required — acceleration becomes the derivative of velocity, and velocity the derivative of position.
Tips & Insights
Deceleration is negative acceleration
If final velocity is less than initial velocity, acceleration is negative (deceleration). The magnitude tells you the rate of slowing. The calculator handles this automatically.
0 to 60 mph conversion
0 to 60 mph = 0 to 26.82 m/s. A car doing 0-60 in 5 seconds accelerates at 26.82/5 = 5.36 m/s² ≈ 0.55g.
Distance formula check
For a sanity check: average velocity = (u+v)/2. Distance = average velocity × time. A car going 0 to 30 m/s in 10s travels (0+30)/2 × 10 = 150 m.
Worked Examples
Car accelerating from rest
0 to 100 km/h (27.78 m/s) in 8 seconds: acceleration = 3.47 m/s² (0.35g). Distance covered: 111 m.
Emergency braking
Stopping from 20 m/s (72 km/h) in 2 seconds: acceleration = −10 m/s² (≈1g deceleration). Distance: 20 m.
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Frequently Asked Questions
What is acceleration?
Acceleration is the rate of change of velocity — how quickly an object speeds up, slows down, or changes direction. Unit: m/s².
What does negative acceleration mean?
Negative acceleration (deceleration) means the object is slowing down. If moving in the positive direction, a negative acceleration reduces speed.
What is 1g of acceleration?
1g equals Earth's gravitational acceleration: 9.81 m/s². An object in free fall near Earth's surface accelerates at 1g (ignoring air resistance).
How is acceleration related to force?
By Newton's Second Law: F = ma. Force equals mass times acceleration. A larger force on the same mass produces greater acceleration.
Can acceleration be zero while moving?
Yes. Constant velocity means zero acceleration. A car cruising at exactly 60 mph on a flat, straight road has zero net acceleration.
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