How to find the magnitude of acceleration? What's the complete method?

The magnitude of acceleration is the absolute value of the acceleration vector, representing how much acceleration exists regardless of direction. For one-dimensional motion, simply calculate a = (v - u) / t and take the absolute value: |a|. If a car decelerates at -6 m/s², the magnitude is 6 m/s². For motion in two or three dimensions, acceleration has multiple components (a_x, a_y, a_z), and the magnitude is found using the Pythagorean theorem: |a| = √(a_x² + a_y² + a_z²).

In two-dimensional problems like projectile motion, you'll often calculate horizontal and vertical components separately, then combine them. A ball thrown at an angle experiences zero horizontal acceleration (a_x = 0) and constant downward vertical acceleration (a_y = -9.8 m/s²), giving magnitude |a| = √(0² + 9.8²) = 9.8 m/s², which equals gravitational acceleration. For a car turning while braking, you might have a_x = -4 m/s² (braking) and a_y = 2 m/s² (centripetal toward curve center), yielding |a| = √(16 + 4) = 4.47 m/s².

The complete method requires three steps: identify all acceleration components, square each component, then sum and take the square root. For circular motion at constant speed, centripetal acceleration a_c = v²/r points toward the center, and since tangential acceleration is zero (speed isn't changing), the magnitude equals a_c directly. Always distinguish between magnitude (scalar, always positive) and the acceleration vector itself (includes direction information). GPS systems report acceleration magnitude when displaying "g-forces" during driving, while engineering analysis requires full vector components for design calculations.