How do you calculate acceleration?

Acceleration is calculated using the formula a = (v - v0) / t, where v is final velocity, v0 is initial velocity, and t is time. Alternatively, use a = (v2 - v02) / 2d when distance is known instead of time.

G-force is a measure of acceleration relative to Earth's gravity. 1g equals 9.81 m/s2. At 2g, you experience twice your normal weight. Fighter pilots can experience up to 9g during extreme maneuvers.

What is the difference between angular and linear acceleration?

Linear acceleration measures change in straight-line velocity (m/s2), while angular acceleration measures change in rotational velocity (rad/s2). They are related by the radius: tangential acceleration = angular acceleration times radius.

Acceleration Calculator | Linear, Angular, G-Force Calculator

Acceleration Equations

a = (v - v0) / t

Linear Acceleration

a = (v2 - v02) / 2d

From Distance

alpha = (omega_f - omega_i) / t

Angular Acceleration

G = a / 9.81

G-Force Conversion

Instantaneous Acceleration Calculator

Find instantaneous acceleration from position function using calculus (derivatives). Select a predefined function or enter your own.

Position Function x(t) Position as a function of time

t - Time Value (seconds) Evaluate at this time

Reset

Complete Guide to Acceleration Calculations

This free acceleration calculator helps you solve physics problems involving linear acceleration, angular acceleration, g-forces, and instantaneous acceleration. Perfect for students, engineers, and physics enthusiasts.

What is Acceleration?

Acceleration is the rate of change of velocity over time. It is a vector quantity with both magnitude and direction.

Key formulas:

a = (v - v0) / t (average acceleration)
a = dv/dt (instantaneous acceleration)
Units: meters per second squared (m/s2)

Positive acceleration means speeding up in the direction of motion. Negative acceleration (deceleration) means slowing down.

Understanding G-Forces

G-force measures acceleration relative to Earth's gravity (g = 9.81 m/s2). At 1g, you experience normal weight. Higher g-forces multiply the apparent weight.

G-force effects on humans:

1g - Normal standing weight
2-3g - Increased effort to move, heavy feeling
4-6g - Difficulty breathing, tunnel vision begins
7-9g - Risk of blackout without g-suit
10g+ - Extremely dangerous, potential injury

Angular vs Linear Acceleration

Linear acceleration describes change in straight-line velocity. Angular acceleration describes change in rotational velocity.

Key relationships:

Tangential acceleration: a_t = alpha * r
Centripetal acceleration: a_c = omega^2 * r = v^2 / r
Total acceleration: a = sqrt(a_t^2 + a_c^2)

Angular acceleration is measured in radians per second squared (rad/s2).

Real-World Applications

Automotive: 0-60 mph times, braking distances
Aerospace: Rocket launches, aircraft maneuvers
Sports: Sprint starts, ball impacts
Engineering: Elevator design, crash testing
Theme Parks: Roller coaster g-forces
Medicine: Centrifuge training, impact injury analysis

Instantaneous Acceleration

Instantaneous acceleration is the acceleration at a specific moment in time. It is found using calculus - taking the second derivative of position with respect to time.

Process:

Start with position function x(t)
Find velocity: v(t) = dx/dt (first derivative)
Find acceleration: a(t) = dv/dt = d2x/dt2 (second derivative)
Substitute the specific time value