Acceleracions

Acceleracions, usually called accelerations in English, describe the rate at which an object's velocity changes over time. It is a vector quantity, meaning it has both magnitude and direction. In SI units, acceleration is measured in meters per second squared (m/s^2).

Mathematically, acceleration a is the time derivative of velocity v: a = dv/dt. For a finite interval, the average acceleration is Δv/Δt; instantaneous acceleration is the limit as Δt approaches zero.

Acceleration relates to force through Newton's second law: F = m a for a body of mass m under net external force F. The acceleration vector points in the direction of the net force (for constant mass).

In one-dimensional motion with constant acceleration, the kinematic equations include: v = v0 + a t; x = x0 + v0 t + 1/2 a t^2; v^2 = v0^2 + 2 a (x − x0).

In more general motion, acceleration has components along a chosen basis: a = (ax, ay, az). For circular motion, the tangential and centripetal components are a_t = r α and a_c = ω^2 r, where α is angular acceleration and ω is angular velocity.

Relativistic considerations distinguish coordinate acceleration from proper acceleration; as speeds approach light, the classical formulas break down, and no object with mass can reach c. Accelerometers measure proper acceleration.

Applications span vehicle dynamics, aerospace, crash analysis, and robotics, where accelerations determine forces, stability, and control. Examples include a car speeding up on a highway or a satellite changing its velocity in orbit.