Acceleration Calculator
Calculate acceleration, velocity, time, or distance using kinematic equations. Supports unit conversions and step-by-step physics solutions.
Acceleration Calculator
Calculator
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Formula: a = (vf - v₀) / t | d = v₀t + ½at² | vf² = v₀² + 2ad
Worked example — a = 3.47 m/s² (0.354g) | d = 111.11 m
Formula
a = (vf - v₀) / t | d = v₀t + ½at² | vf² = v₀² + 2ad
The kinematic equations describe motion with constant acceleration. a = (vf - v₀)/t finds acceleration. d = v₀t + ½at² finds displacement. vf = v₀ + at finds final velocity. vf² = v₀² + 2ad relates velocity and distance without time.
Worked Examples
Example 1: Car Acceleration
Problem:A car accelerates from 0 to 100 km/h (27.78 m/s) in 8 seconds. Find the acceleration and distance.
Solution:a = (vf - v₀) / t = (27.78 - 0) / 8 = 3.47 m/s² a = 0.354g d = v₀t + ½at² = 0 + ½(3.47)(64) = 111.11 m
Result:a = 3.47 m/s² (0.354g) | d = 111.11 m
Example 2: Braking Distance
Problem:A car traveling at 30 m/s brakes with deceleration of -6 m/s². How far does it travel before stopping?
Solution:v₀ = 30 m/s, vf = 0 m/s, a = -6 m/s² d = (vf² - v₀²) / (2a) = (0 - 900) / (-12) = 75 m t = (vf - v₀) / a = (0 - 30) / (-6) = 5 s
Result:Braking distance: 75 m | Time to stop: 5 s
Frequently Asked Questions
What is acceleration?
Acceleration is the rate of change of velocity over time, measured in meters per second squared (m/s²). Positive acceleration means speeding up, negative acceleration (deceleration) means slowing down. The formula is a = (vf - v₀) / t, where vf is final velocity, v₀ is initial velocity, and t is time. For example, a car going from 0 to 60 mph (26.8 m/s) in 5 seconds has an acceleration of 5.36 m/s², or about 0.55 g.
What are the kinematic equations?
The four kinematic equations for constant acceleration are: (1) vf = v₀ + at, (2) d = v₀t + ½at², (3) vf² = v₀² + 2ad, (4) d = ½(v₀ + vf)t. Each equation relates four of the five kinematic variables (v₀, vf, a, t, d). Given any three known values, you can find the other two. These equations assume constant (uniform) acceleration and straight-line motion.
What is the difference between speed and velocity?
Speed is a scalar quantity — it only has magnitude (how fast something moves, e.g., 50 km/h). Velocity is a vector quantity — it has both magnitude and direction (e.g., 50 km/h north). An object moving in a circle at constant speed has changing velocity because its direction constantly changes, which means it's accelerating (centripetal acceleration). In kinematic equations, we use velocity because direction matters for determining position.
How do I convert between velocity units?
Common velocity conversions: 1 m/s = 3.6 km/h = 2.237 mph = 3.281 ft/s. To convert km/h to m/s, divide by 3.6. To convert mph to m/s, multiply by 0.44704. For example, 100 km/h = 27.78 m/s = 62.14 mph. These conversions are essential when applying kinematic equations, which typically use SI units (m, s, m/s, m/s²).
Which kinematic equation should I use when the time is unknown?
Use vf squared = v0 squared + 2ad, the only one of the four equations that omits time. It links the two velocities, the acceleration and the displacement directly. For a car at 30 m/s braking at 5 m/s squared to a stop, the stopping distance is 900 divided by 10, that is 90 m. Rearranged the same way, it also gives the acceleration needed to reach a speed within a set distance.
What is the difference between average and instantaneous acceleration?
Average acceleration is the total change in velocity divided by the total elapsed time, which is what Acceleration Calculator returns. Instantaneous acceleration is the derivative of velocity with respect to time, the value at one moment, and it is what an accelerometer measures. The two agree only when the acceleration is constant; during a gear change or a braking release they can differ substantially.
Does a negative acceleration always mean the object is slowing down?
No. The sign of acceleration gives its direction along the chosen axis, not whether the object is speeding up. An object is slowing only when acceleration opposes velocity. A ball moving in the negative direction with negative acceleration is speeding up. Use deceleration to describe the physical effect and reserve the minus sign for direction relative to your coordinate axis.
How do the kinematic equations apply to free fall?
Substitute the acceleration due to gravity, about 9.80665 m/s squared, directed downward, and neglect air resistance. An object released from rest reaches roughly 29.4 m/s after 3 s and falls about 44.1 m in that time. Drag breaks the constant-acceleration assumption once speed grows, and at terminal velocity the acceleration is zero even though the object is still moving fast.
What do the slope and the area of a velocity-time graph represent?
The slope of a velocity-time graph is the acceleration, and the area between the curve and the time axis is the displacement. Under constant acceleration the shape is a trapezium whose area is one half of the sum of the initial and final velocities times the elapsed time, which is exactly the fourth kinematic equation. Areas below the axis count as negative displacement.
Why do these equations fail when the acceleration is not constant?
Every one of the four equations is derived on the assumption that acceleration is uniform over the interval. With aerodynamic drag, a changing thrust or a variable braking force the acceleration depends on speed or time, and the formulas give wrong answers. The usual remedies are to integrate the actual acceleration function or to split the motion into short intervals where a constant value is a fair approximation.
References
Background & Theory
Acceleration and G-Force in Context
Acceleration only becomes intuitive once it's compared to a familiar reference — and the most useful reference is g, Earth's gravitational acceleration of 9.80665 m/s^2, which is what your body feels as ordinary weight at rest.
| Scenario | Approx. acceleration |
|---|---|
| Typical sedan, 0-100 km/h in 8s | ~0.35g (3.47 m/s^2) |
| Sports car, 0-100 km/h in 3s | ~0.94g (9.26 m/s^2) |
| Emergency braking (dry pavement) | ~0.7-1.0g |
| Typical roller coaster peak | 3-5g (brief) |
| Fighter pilot sustained turn limit | ~9g (with G-suit) |
Human tolerance to acceleration depends heavily on direction and duration — brief peaks well above 9g are survivable (crash-test data and rocket-sled experiments have recorded over 40g for milliseconds), but sustained acceleration above roughly 5g causes most people to gray out or black out as blood is forced away from the brain.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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