Solve equations of motion for constant acceleration - enter any 3 values to find the rest
Enter at least 3 known values to calculate the missing variables
SUVAT is an acronym representing five fundamental variables in kinematics: s (displacement), u (initial velocity), v (final velocity), a (acceleration), and t (time). These equations form the mathematical foundation for analyzing motion with constant acceleration.
The SUVAT equations are derived from the basic definitions of velocity and acceleration using calculus. They provide a powerful toolkit for solving a wide range of physics problems, from calculating how long it takes a car to brake to a complete stop, to determining the maximum height reached by a launched projectile, to analyzing the motion of falling objects.
These equations are only valid when acceleration is constant. For scenarios with changing acceleration, such as rocket launches or objects experiencing variable drag forces, more advanced techniques using calculus or numerical methods are required. Understanding when SUVAT applies and when it doesn't is crucial for accurate physics problem-solving.
Step 1: Identify the known values from your problem. You need at least three of the five SUVAT variables (s, u, v, a, t) to solve for the remaining ones. Read the problem carefully to extract these values.
Step 2: Enter the known values in their respective fields. Leave the unknown values blank. The calculator uses an iterative algorithm to solve all four SUVAT equations simultaneously until all variables are determined.
Step 3: Review the calculated results. All five variables will be displayed with high precision. Verify that the results make physical sense for your problem (e.g., time should generally be positive).
A car traveling at 20 m/s begins braking with a constant deceleration of -5 m/s². How far does the car travel before coming to a complete stop, and how long does this take?
The car travels 40 meters before coming to a complete stop, taking 4 seconds to do so. This calculation is critical for understanding safe following distances and braking requirements in traffic safety engineering.
SUVAT equations only apply when acceleration is constant. If acceleration changes over time (like a rocket burning fuel or a car accelerating variably), you must use calculus-based methods or numerical integration instead.
Distance is a scalar quantity measuring total path length. Displacement (s) is a vector quantity measuring the straight-line change in position from start to finish. SUVAT uses displacement, not distance.
Each SUVAT equation contains 4 of the 5 variables. To solve for unknowns, you need 3 known values to create enough equations. With fewer knowns, the system is underdetermined and has infinite solutions.
In standard physics problems, time is positive. A negative result typically indicates an event before the defined start time (t=0), or may suggest you should choose the positive root when solving quadratic equations.
Negative displacement simply means the object moved in the negative direction (opposite to your chosen positive direction). It's perfectly valid - displacement is a vector with both magnitude and direction.
For free fall near Earth's surface, use a = -9.8 m/s² (or +9.8 m/s² if downward is positive). SUVAT works perfectly for free fall since gravitational acceleration is constant (ignoring air resistance).
SUVAT equations are used in automotive safety (braking distances), sports physics (ball trajectories), aerospace engineering (rocket launches), and accident reconstruction. They're fundamental to introductory physics courses worldwide.
Different equations are useful depending on which variables you know. For example, if time isn't given, use v² = u² + 2as. Each equation provides a shortcut for specific problem types without needing to solve intermediate steps.
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