Constant velocity vs constant acceleration: what they are
Kinematics studies motion without worrying about its causes (forces). The two simplest motions are:
Uniform Motion — Constant Velocity
Constant velocity. No acceleration. Straight path. A single equation:
s = s₀ + v · t
Examples: a car on a straight road at a fixed speed, an airport moving walkway, light in a vacuum.
Uniformly Accelerated Motion — Constant Acceleration
Constant acceleration (positive or negative). Velocity changes linearly with time. Three useful equations:
Eq. 1 → v = v₀ + a · t (velocity as a function of time) Eq. 2 → s = s₀ + v₀·t + ½ · a · t² (position as a function of time) Eq. 3 → v² = v₀² + 2 · a · Δs (Torricelli — no time!)
Examples: free fall (a = g = 9.8 m/s²), a car braking, a rocket taking off.
When should you use Torricelli's equation?
When the problem does not give the time but you know the acceleration and the displacement. It is the "shortcut" of accelerated motion.
Frequently asked questions
What is the difference between velocity and acceleration?
Velocity is the rate of change of position (m/s). Acceleration is the rate of change of velocity (m/s²). A body in uniform motion has non-zero velocity but zero acceleration.
When is acceleration negative?
When it points in the opposite direction to the velocity — the body is slowing down. In free fall, acceleration is negative if we take the upward direction as positive.
What does Δs mean?
Δs is the displacement — the difference between the final and the initial position: Δs = s − s₀.
Why does Torricelli's equation not include time?
It combines Eq. 1 and Eq. 2 of accelerated motion, eliminating t. It is useful when the time is unknown or irrelevant.
Is the Earth's gravity (g) constant?
Practically yes, near the surface. g ≈ 9.8 m/s² (it varies slightly between 9.78 at the Equator and 9.83 at the poles). For high school calculations 10 m/s² is often used.
Does the calculator accept negative signs?
Yes. Use a negative sign for velocities, positions or accelerations in the direction opposite to the one you defined as positive.