Kinematics Calculator (SUVAT)
Choose which quantity to find and which equation fits what you know. Only the inputs named in your choice are used; the others are ignored. Impossible set-ups are rejected.
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Formula
For constant acceleration in a straight line, with displacement s, initial speed u, final speed v, acceleration a and time t:
v = u + ats = ut + ½at²s = ½(u + v)tv² = u² + 2as
The calculator picks the rearrangement for the quantity you choose. When time is the unknown and s = ut + ½at² is used, it solves the quadratic ½a·t² + u·t − s = 0 and takes the earliest non-negative root. A negative v², a negative time or a division by zero is reported as an error. When v is found from v² = u² + 2as, the positive root is returned.
Worked example
A car at u = 5 m/s accelerates at a = 2 m/s² for t = 3 s.
- Final speed: v = 5 + 2 × 3 = 11 m/s.
- Distance: s = 5 × 3 + ½ × 2 × 3² = 15 + 9 = 24 m.
- Speed after 50 m instead: v = √(5² + 2 × 2 × 50) = √225 = 15 m/s.
Frequently asked questions
What are the SUVAT equations?
They link displacement s, initial speed u, final speed v, acceleration a and time t when acceleration is constant: v = u + at, s = ut + ½at², s = ½(u + v)t and v² = u² + 2as. Each leaves out one of the five variables.
How do I choose the right equation?
List the three values you know and the one you want. Use the equation that contains exactly those four and leaves out the fifth. With u = 5 m/s, a = 2 m/s² and t = 3 s, v = u + at = 5 + 6 = 11 m/s.
When do the SUVAT equations not apply?
Only when acceleration is constant along a straight line. They fail for changing acceleration such as drag at high speed or a rocket burning fuel.
Why does the calculator reject some inputs?
Some set-ups cannot happen. With u = 5 m/s and a = −5 m/s², v² = 25 + 2 × (−5) × 50 is negative, so the object stops before 50 m and never reaches that distance. Time is also never negative.