Kinematics Solver

Enter any three of the five kinematic variables and solve for the remaining two. See step-by-step substitution into the standard equations, along with position, velocity, and acceleration graphs. All calculations run in your browser.

Displacement (s)m

Initial Velocity (u)m/s

Final Velocity (v)m/s

Acceleration (a)m/s²

Time (t)s

Select exactly 3 known variables. The other 2 will be calculated.

Motion Graphs

Position vs Time

Velocity vs Time

Acceleration vs Time

m/s

m/s²

Step-by-Step Solution

Reference Guide

The Kinematic Equations

Four equations relate the five variables of constant-acceleration motion: displacement ( $s$ ), initial velocity ( $u$ ), final velocity ( $v$ ), acceleration ( $a$ ), and time ( $t$ ). Each equation omits one variable, so knowing any three lets you solve for the other two.

v = u + at

s = ut + \frac{1}{2}at^2

v^2 = u^2 + 2as

s = \frac{1}{2}(u + v)t

These equations only apply when acceleration is constant throughout the motion. For varying acceleration, you need calculus-based methods instead.

Choosing the Right Equation

Start by listing the three quantities you know and the one you want to find. Then pick the equation that contains exactly those four variables.

For example, if you know $u$ , $a$ , and $t$ and want $s$ , use $s = ut + \frac{1}{2}at^2$ because it contains all four and leaves out $v$ , which you do not need.

If you know three variables and need both remaining unknowns, solve two equations in sequence. Find one unknown first, then substitute into a second equation for the other.

Always check your answer by substituting back into a different equation. If the values are consistent, the solution is correct.

Common Scenarios

Freefall

Set $a = g = 9.81 \text{ m/s}^2$ downward. An object dropped from rest has $u = 0$ , so the equations simplify considerably.

Braking

Acceleration is negative (opposing the direction of motion). The object slows until $v = 0$ or until you find the stopping distance from $v^2 = u^2 + 2as$ .

Vertical throw

For an object thrown upward, take upward as positive. Then $a = -g$ throughout the flight. At the peak, $v = 0$ . On the way down the object accelerates in the positive-downward direction.

Reading Motion Graphs

Position vs time

The slope at any point equals the velocity. For constant acceleration the curve is parabolic. A steeper slope means faster motion.

Velocity vs time

The slope equals the acceleration. The area under the curve between two times equals the displacement during that interval. A straight line means constant acceleration.

Acceleration vs time

For constant-acceleration problems this graph is a horizontal line. If acceleration changes, the kinematic equations no longer apply and you need a different approach.