SUVAT Third Equation Calculator (v² = u² + 2as)
SUVAT Third Equation Calculator (v² = u² + 2as)
This is the third SUVAT equation of motion, uniquely useful because it relates velocity, acceleration, and displacement without needing to know the time elapsed. Choose which variable to solve for, enter the other three, and this calculator computes the answer.
This is the only one of the three SUVAT equations that leaves out time entirely, which makes it the right tool specifically when a problem gives you velocities, acceleration, and a distance but doesn't mention (or ask for) how long the motion took. Starting from rest with 5 m/s² of acceleration over a 40 m displacement gives a final velocity of 20 m/s — and because the equation involves velocity squared, solving for velocity always requires a square root, so results are only meaningful for the positive root that matches the physical direction of motion.
- v² = u² + 2as, so starting from rest (u = 0) with 5 m/s² of acceleration over a displacement of 40 m gives v = √(2×5×40) = 20 m/s.
- This is the only SUVAT equation without a time variable - useful whenever a problem gives you velocities, acceleration, and distance but not time.
- Solving for u or v involves a square root, so this calculator always returns the positive root - if the calculation is physically impossible (a negative number under the square root), it reports no solution.
How do I use v² = u² + 2as?
Rearrange the equation to solve for whichever variable is unknown - for example v = √(u² + 2as) when solving for final velocity.
What is the final velocity starting from rest with 5 m/s² of acceleration over 40 m?
v = √(0² + 2×5×40) = √400 = 20 m/s.
SUVAT Third Equation Calculator (v² = u² + 2as)
This is the third SUVAT equation of motion, uniquely useful because it relates velocity, acceleration, and displacement without needing to know the time elapsed. Choose which variable to solve for, enter the other three, and this calculator computes the answer.
This is the only one of the three SUVAT equations that leaves out time entirely, which makes it the right tool specifically when a problem gives you velocities, acceleration, and a distance but doesn't mention (or ask for) how long the motion took. Starting from rest with 5 m/s² of acceleration over a 40 m displacement gives a final velocity of 20 m/s — and because the equation involves velocity squared, solving for velocity always requires a square root, so results are only meaningful for the positive root that matches the physical direction of motion.
- v² = u² + 2as, so starting from rest (u = 0) with 5 m/s² of acceleration over a displacement of 40 m gives v = √(2×5×40) = 20 m/s.
- This is the only SUVAT equation without a time variable - useful whenever a problem gives you velocities, acceleration, and distance but not time.
- Solving for u or v involves a square root, so this calculator always returns the positive root - if the calculation is physically impossible (a negative number under the square root), it reports no solution.
How do I use v² = u² + 2as?
Rearrange the equation to solve for whichever variable is unknown - for example v = √(u² + 2as) when solving for final velocity.
What is the final velocity starting from rest with 5 m/s² of acceleration over 40 m?
v = √(0² + 2×5×40) = √400 = 20 m/s.