Acceleration Calculator

The Five SUVAT Equations

For uniform acceleration, five equations relate the five variables (s=distance, u=initial velocity, v=final velocity, a=acceleration, t=time). v = u + at. s = ut + ½at². s = vt − ½at². v² = u² + 2as. s = ½(u+v)t. Any two known values allow you to calculate the other three. Named after their variables, these equations are fundamental to classical mechanics and form the core of GCSE and A-level physics.

Free Fall and g

Near Earth's surface, objects in free fall (ignoring air resistance) accelerate at g = 9.81 m/s². Dropped from rest: after 1 second a speed of 9.81 m/s, after 2 seconds 19.62 m/s, falling 4.9 m in the first second and 19.6 m in the first two seconds. Terminal velocity occurs when air resistance equals gravitational force — approximately 53 m/s (190 km/h) for a typical human skydiver in the belly-to-earth position, higher in the head-down position.

Real-World Examples

A car accelerating from 0 to 60 mph (26.8 m/s) in 6 seconds: a = 26.8/6 = 4.47 m/s². That is 0.46g (gravity equivalents). A fighter jet can sustain 9g briefly. An airliner at takeoff experiences approximately 0.3g. A passenger braking emergency stop (0.8g) is approximately 7.8 m/s². The Large Hadron Collider accelerates protons to 0.9999% the speed of light — the SUVAT equations no longer apply at relativistic speeds; Einstein's equations are needed.

Limitations of SUVAT

SUVAT equations assume constant (uniform) acceleration — they cannot model variable acceleration without calculus. Real-world situations like a car accelerating (changing gear, engine power curve) or a falling object (air resistance increasing with speed) require integration of the force equation over time. For many practical engineering and physics problems, however, assuming constant acceleration over short time intervals gives adequately accurate results.