Understanding SUVAT Equations
Educational Tool
The SUVAT equations are fundamental in classical mechanics for describing motion under constant acceleration. They're used extensively in physics education and form the basis for understanding more complex motion problems. This tool helps you solve these equations and understand the step-by-step process.
The Five SUVAT Equations
v = u + at
Final velocity equals initial velocity plus acceleration times time.Missing variable: s
s = (u + v)/2 × t
Displacement equals average velocity times time.Missing variable: a
s = ut + ½at²
Displacement with initial velocity and acceleration.Missing variable: v
s = vt - ½at²
Displacement with final velocity and acceleration.Missing variable: u
v² = u² + 2as
Time-independent equation relating velocities, acceleration, and displacement.Missing variable: t — Very useful for braking distance calculations!
Variable Definitions
- s = Displacement (m or ft) — change in position, NOT distance traveled
- u = Initial velocity (m/s or ft/s) — velocity at time t = 0
- v = Final velocity (m/s or ft/s) — velocity at time t
- a = Acceleration (m/s² or ft/s²) — must be constant
- t = Time (s) — duration of the motion
Sign Conventions
- Choose a positive direction (e.g., right, up, forward)
- Motion in the positive direction: u, v > 0
- Motion in the negative direction: u, v < 0
- Speeding up: a has same sign as velocity
- Slowing down: a has opposite sign to velocity
- Time is always positive (forward in time)
Common Applications
- • u = 0 (starting from rest)
- • Given a and t, find v and s
- • Example: 0-60 mph acceleration tests
- • v = 0 (coming to a stop)
- • Given u and a (negative), find s
- • Use v² = u² + 2as for quick solving
- • a = g ≈ 9.8 m/s² (or -9.8 if up is positive)
- • Dropping: u = 0, find v after falling height s
- • Throwing up: find max height when v = 0
- • Compare multiple objects with different a, u
- • Find when/where they meet (same s at same t)
- • Multi-case mode helps compare scenarios
Important Limitations
- Constant acceleration only: SUVAT equations assume acceleration doesn't change during the motion. For variable acceleration, calculus is needed.
- 1D motion only: These equations apply to motion in a straight line. For 2D motion (like projectiles), apply SUVAT separately to each component.
- No air resistance: Real-world motion often involves drag forces that make acceleration non-constant. These equations ignore such effects.
- Educational purposes: This tool is for learning and practice. For engineering applications, consider additional factors and safety margins.
Frequently Asked Questions
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