SUVAT Calculator

The SUVAT Calculator solves the five fundamental equations of uniformly accelerated motion, collectively known as the SUVAT equations. These equations relate displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t) for any object moving with constant acceleration in a straight line.

The five SUVAT equations are derived from the basic definitions of velocity and acceleration through calculus or algebraic methods. They are: $$v = u + at$$, $$s = ut + \tfrac{1}{2}at^2$$, $$s = vt - \tfrac{1}{2}at^2$$, $$v^2 = u^2 + 2as$$, and $$s = \tfrac{1}{2}(u + v)t$$. Each equation connects four of the five variables, making it possible to find any unknown variable given three known ones.

These equations form the backbone of classical kinematics and apply wherever acceleration is constant. Common applications include free-fall problems (where $$a = g \approx 9.81\,\text{m/s}^2$$), vehicles accelerating or braking on flat roads, objects sliding down inclined planes with constant friction, and projectile motion when broken into horizontal and vertical components.

The SUVAT framework is powerful because it provides two independent equations for each unknown, allowing cross-verification. If both equations yield the same result, the input values are consistent. When the discriminant in equations involving square roots becomes negative, this indicates physically impossible conditions—the object cannot reach the specified state under the given constraints.

Understanding SUVAT equations is essential for students and engineers working with linear motion problems. They underpin more complex analyses including multi-stage motion, relative motion between objects, and serve as the linearized approximation for systems with slowly varying acceleration. For non-constant acceleration, these equations must be replaced by their integral calculus counterparts.

Sign conventions are critical when applying SUVAT equations. Typically, the direction of initial motion is taken as positive. When dealing with vertical motion, upward is often positive, making gravitational acceleration negative ($$a = -9.81\,\text{m/s}^2$$). Displacement can be negative, indicating motion in the opposite direction from the chosen positive axis.