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How It Works
The constant-acceleration kinematics equations describe motion in a straight line when acceleration does not change. The velocity equation v = v₀ + at gives the final speed, the average velocity equation vₐᵥᵍ = (v₀ + v)/2 gives the mean speed, and the displacement equation Δx = vₐᵥᵍ · t tells you how far the object travels.
These three formulas cover free-fall, braking distances, and any scenario where acceleration stays constant over the time interval of interest.
Example Problem
A car starts from rest (v₀ = 0) and accelerates at 3 m/s² for 5 seconds.
- v = 0 + 3 × 5 = 15 m/s
- vₐᵥᵍ = (0 + 15) / 2 = 7.5 m/s
- Δx = 7.5 × 5 = 37.5 m
Frequently Asked Questions
What does constant acceleration mean?
Constant acceleration means the velocity changes by the same amount each second. Free-fall near Earth's surface (a = 9.81 m/s²) is the most common example.
How do you calculate braking distance?
Use Δx = vₐᵥᵍ · t. A car at 30 m/s decelerating at −6 m/s² stops in 5 s, with vₐᵥᵍ = 15 m/s and Δx = 15 × 5 = 75 m.
Can acceleration be negative?
Yes. Negative acceleration (deceleration) means the object is slowing down in the positive direction. Always use a consistent sign convention for direction.
When can't you use these equations?
These equations only apply when acceleration is constant. If acceleration changes over time (e.g., a rocket burning fuel), you need calculus-based kinematics instead.
Related Calculators
- Projectile Motion Calculator — extend kinematics to two-dimensional motion.
- Force Equation Calculator — find the force causing the acceleration.
- Gravity Equations Calculator — calculate gravitational acceleration (free-fall).
- Kinetic Energy Calculator — find the energy of a moving object from mass and velocity.
- Acceleration Converter — convert between m/s², ft/s², g, and other acceleration units.
Reference: Tipler, Paul A. 1995. Physics For Scientists and Engineers. Worth Publishers. 3rd ed.