Acceleration Calculator

Calculate acceleration using a = Deltav/Deltat. Enter initial velocity, final velocity, and time to determine acceleration or deceleration.

Basic Acceleration Formula: a = Deltav / Deltat = (v_f - v_i) / t Where: ? a = Acceleration (m/s^2, ft/s^2, g) ? Deltav = Change in velocity (v_final - v_initial) ? v_f = Final velocity (m/s) ? v_i = Initial velocity (m/s) ? t = Time interval (s) Related Formulas: ? Final velocity: v_f = v_i + at ? Distance: d = v_i?t + ?at^2 ? Velocity-distance: v_f^2 = v_i^2 + 2ad Unit Conversions: ? 1 m/s^2 = 3.281 ft/s^2 ? 1 m/s^2 = 0.102 g (where g = 9.8 m/s^2) ? 1 g = 9.80665 m/s^2 Special Cases: ? Positive a: speeding up (in positive direction) ? Negative a: slowing down (deceleration) ? a = 0: constant velocity (no acceleration)
Example 1 - Car Acceleration: Initial velocity = 0 m/s, Final velocity = 27.78 m/s (100 km/h), Time = 6 s a = (27.78 - 0) / 6 = 4.63 m/s^2 = 0.47 g Car accelerates at 4.63 m/s^2. Example 2 - Emergency Braking: Initial velocity = 30 m/s, Final velocity = 0 m/s, Time = 5 s a = (0 - 30) / 5 = -6 m/s^2 (deceleration) Car decelerates at 6 m/s^2 (negative = slowing down). Example 3 - Free Fall (gravity): Initial velocity = 0 m/s, Final velocity = 49 m/s, Time = 5 s a = (49 - 0) / 5 = 9.8 m/s^2 = 1 g Gravitational acceleration on Earth. Example 4 - Rocket Launch: Initial velocity = 0 m/s, Final velocity = 100 m/s, Time = 10 s a = (100 - 0) / 10 = 10 m/s^2 = 1.02 g Rocket accelerates at 10 m/s^2. Example 5 - Train Slowing: Initial velocity = 25 m/s, Final velocity = 15 m/s, Time = 20 s a = (15 - 25) / 20 = -0.5 m/s^2 Train decelerates gradually at 0.5 m/s^2.

What is acceleration?

Acceleration is the rate of change of velocity with respect to time. It measures how quickly an object speeds up, slows down, or changes direction. The formula is a = Deltav/Deltat = (v_final - v_initial)/time. It's a vector quantity with both magnitude and direction.

What is the difference between uniform and non-uniform acceleration?

Uniform (constant) acceleration means velocity changes at a constant rate (a = constant), like free fall under gravity. Non-uniform acceleration means the rate of velocity change varies with time, like a car in city traffic. This calculator assumes uniform acceleration.

Can acceleration be negative?

Yes, negative acceleration (often called deceleration or retardation) indicates the object is slowing down in the positive direction, or speeding up in the negative direction. For example, a = -5 m/s^2 means velocity decreases by 5 m/s each second.

What is the difference between acceleration and deceleration?

Deceleration is negative acceleration - when an object slows down. If a car's velocity decreases from 20 m/s to 10 m/s in 2 seconds, a = (10-20)/2 = -5 m/s^2. The negative sign indicates deceleration. Both are acceleration, just in opposite directions.

What is gravitational acceleration?

Gravitational acceleration (g) is the acceleration of objects in free fall near Earth's surface, approximately 9.8 m/s^2 or 32.2 ft/s^2 downward. This means falling objects increase velocity by 9.8 m/s every second (ignoring air resistance). On other planets, g differs.

What are common units for acceleration?

Common units include: m/s^2 (meters per second squared - SI unit), ft/s^2 (feet per second squared), km/h/s (kilometers per hour per second), and g (gravitational units, where 1g = 9.8 m/s^2). Racing and aviation often use g-forces.

How do I convert between acceleration units?

Key conversions: 1 m/s^2 = 3.28 ft/s^2 = 0.102 g. To convert m/s^2 to ft/s^2, multiply by 3.28. To convert to g-forces, divide by 9.8. For km/h/s to m/s^2, divide by 3.6. Example: 20 m/s^2 = 2.04 g (strong acceleration).

What is centripetal acceleration?

Centripetal acceleration is the acceleration toward the center of a circular path, given by a = v^2/r, where v is tangential velocity and r is radius. Even at constant speed, circular motion involves acceleration because direction changes. Example: cars turning corners.

How does acceleration relate to force?

Newton's Second Law: F = ma. Force equals mass times acceleration. A larger force produces greater acceleration (for same mass), and a larger mass requires more force for the same acceleration. Example: 1000 N force on 500 kg mass gives a = 2 m/s^2.

What are real-world examples of acceleration?

Examples: car acceleration (0-60 mph time), rocket launches (high positive acceleration), emergency braking (high negative acceleration), elevators starting/stopping, roller coasters, athletic sprints, and aircraft takeoff. Sports cars can achieve 0-60 mph in ~3 seconds (a ~= 9 m/s^2).

What is the difference between linear and angular acceleration?

Linear acceleration (a) is the rate of change of linear velocity (m/s^2). Angular acceleration (alpha) is the rate of change of angular velocity (rad/s^2). They're related by a = alphar for circular motion, where r is radius. This calculator handles linear acceleration.

How do I calculate distance traveled during acceleration?

Use kinematic equations: d = v0t + ?at^2 (with initial velocity) or d = (v^2 - v0^2)/(2a) (without time). Example: starting from rest (v0=0) with a=5 m/s^2 for 4 seconds: d = 0 + ?(5)(4^2) = 40 meters.