Equations of Motion (SUVAT) Calculator
Starting from rest with a = 2 m/s² for 10 s, the body covers a displacement of 100 m and reaches 20 m/s, from s = ut + ½at² and v = u + at.
100 m
- final velocity v
- 20 m/s
Step-by-step solution
- Known: u = 0 m/s, a = 2 m/s², t = 10 s
- s = ut + ½at² = 100 m
- v = u + at = 20 m/s
Equations of Motion (SUVAT) Formula
v = u + at, s = ut + ½at², v² = u² + 2as, s = (u + v)t/2
s displacement, u initial velocity, v final velocity, a acceleration, t time
Worked Example
A body starting from rest (u = 0) with a = 2 m/s² for t = 10 s:
- Known: u = 0 m/s, a = 2 m/s², t = 10 s
- s = ut + ½at² = 100 m
- v = u + at = 20 m/s
Sign convention
Pick one direction as positive and keep it. For a ball thrown upward at 15 m/s, take up as positive: u = 15 m/s and a = −9.81 m/s².
More Motion Calculators
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a = (v − u) / t
a acceleration, v final velocity, u initial velocity, t time taken
Example: A car that speeds up from 5 m/s to 25 m/s in 10 s: Acceleration a = 2 m/s².
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Free Fall Calculator
h = ½ g t², v = g t = √(2gh)
h height fallen, t time, v speed reached, g gravitational acceleration
Example: A stone dropped from 45 m: Fall time t = 3.02943 s.
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Projectile Motion Calculator
R = v₀ cos θ × T, H = h₀ + (v₀ sin θ)²/2g
T = (v₀ sin θ + √((v₀ sin θ)² + 2gh₀))/g; on level ground R = v₀² sin 2θ / g
Example: A ball kicked at 20 m/s and 45° from ground level (g = 9.80665 m/s²): Range R = 40.7886 m.
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Speed Distance Time Calculator
v = d / t
v average speed, d distance, t time; d = v × t, t = d / v
Example: A 150 km drive that takes 2 hours 30 minutes: Speed v = 60 km/h.
Frequently asked questions
When do the SUVAT equations apply?
Only for constant acceleration in a straight line, such as free fall without air resistance or steady braking. For changing acceleration you need calculus.
Which equation should I use?
Pick the one without the quantity you neither know nor want. No t: v² = u² + 2as. No v: s = ut + ½at². No a: s = (u + v)t/2. No s: v = u + at.
Why can there be two answers?
v² = u² + 2as has a ± root: a ball thrown up passes the same height going up and coming down. The calculator gives the first time the body reaches s.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Equations of Motion (SUVAT) Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/equations-of-motion-calculator/
IEEE
Scientific Converters, "Equations of Motion (SUVAT) Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/equations-of-motion-calculator/