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Kinematics equations
They describe the relationships between velocity, acceleration, and displacement, providing the tools to solve a wide range of motion-related physics problems.
v = v₀ + at
Relates final velocity (v) to initial velocity (v₀), acceleration (a), and time (t).
v = v₀ + at
Used for scenarios with uniform acceleration.
Δx = v₀t + ½at²
Calculates displacement (Δx) under constant acceleration.
Δx = v₀t + ½at²
Combines the effects of initial velocity and acceleration over time. Useful for determining distance traveled from rest or with an initial velocity.
v² = v₀² + 2aΔx
Links the squares of velocities to acceleration and displacement.
v² = v₀² + 2aΔx
Helpful when time is unknown or unnecessary. Highlights the connection between kinetic energy and work.
x = x₀ + vt (for constant velocity)
Describes position (x) of an object moving at a constant velocity (v). Shows displacement as directly proportional to time for constant velocity.
v_avg = (v + v₀) / 2
Calculates average velocity (v_avg) for uniformly accelerating objects. Represents the arithmetic mean of initial and final velocities.
v_avg = Δx / Δt
Defines average velocity as total displacement (Δx) divided by total time (Δt).
a = Δv / Δt
Defines acceleration (a) as the rate of change in velocity (Δv) over time (Δt). Indicates how quickly an object accelerates or decelerates.
Δx = v_avg * t
Calculates displacement (Δx) using average velocity (v_avg) and time (t). Works for both constant and variable velocities.
x = ½(v + v₀)t
Computes displacement (x) from the average of initial and final velocities over time.
x = ½(v + v₀)t
Derived from average velocity, suitable for uniformly accelerated motion.
Δy = v₀y * t + ½gt²
for vertical motion under gravity
Δy = v₀y * t + ½gt² (for vertical motion under gravity)
Describes vertical displacement (Δy) under gravity’s influence. Includes initial vertical velocity (v₀y) and gravitational acceleration (g).
Δy = v₀y * t + ½gt²
Crucial for solving projectile motion and free-fall problems.
Δx = v_avg * t
Simplifies distance calculations over a time period.
x = ½(v + v₀)t
Helps determine distance when acceleration is involved.
x = x₀ + vt (for constant velocity)
Used to find an object’s position without acceleration.
Note 
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