Motion Equation Calculator
Calculate final velocity and displacement from initial velocity, acceleration, and time using SUVAT equations.
How it works
- 1Enter the initial velocity (v₀), acceleration (a), and time (t) in either metric or imperial units.
- 2The calculator applies v = v₀ + at to find the final velocity and s = v₀t + ½at² to find the displacement.
- 3Results update instantly in your chosen unit system, with the final speed also converted to km/h or mph.
Use cases
- Physics students checking SUVAT homework problems involving constant-acceleration motion.
- Engineers estimating launch velocity or run-up distance in vehicle and projectile design.
- Sports scientists calculating the speed a sprinter reaches after a set acceleration phase.
Frequently asked questions
What are the four SUVAT equations of motion?
For motion under constant acceleration: (1) v = u + at; (2) s = ut + ½at²; (3) v² = u² + 2as; (4) s = ½(u + v)t. This calculator uses equations 1 and 2. Here u is initial velocity, v is final velocity, a is acceleration, t is time, and s is displacement.
Can you show a worked example?
Yes. A car starts from rest (u = 0) and accelerates at 2 m/s² for 5 s. Using v = u + at: v = 0 + 2 × 5 = 10 m/s. Using s = ut + ½at²: s = 0 + ½ × 2 × 25 = 25 m. The car reaches 10 m/s and travels 25 m.
Do these equations apply to non-constant acceleration?
No. The SUVAT equations assume perfectly constant acceleration throughout the interval. For variable acceleration you need to integrate the acceleration function over time, or use numerical methods.
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