Kinematic Equations of Motion

List given values with units. Convert units if needed. Identify the unknown. Choose the equation that contains the given values and the unknown. Substitute carefully and write the final unit.

A small table of u, v, a, t, and s can support formula selection; a velocity-time graph may be used to derive or connect the equations.

Using s = vt instead of s = ut + 1/2 at² in accelerated motion is wrong because velocity is changing.

Kinematic equations of motion are formulae used to connect initial velocity, final velocity, acceleration, time, and displacement for uniformly accelerated motion.

Kinematic equations of motion are formulae used to connect initial velocity, final velocity, acceleration, time, and displacement for uniformly accelerated motion. v = u + at; s = ut + 1/2 at²; v² = u² + 2as. Here u is initial velocity, v is final velocity, a is uniform acceleration, t is time, and s is displacement. If a scooter starts from rest and accelerates at 2 m/s² for 5 s, v = u + at = 0 + 2 × 5 = 10 m/s.

The three common equations are v = u + at, s = ut + 1/2 at², and v² = u² + 2as. They should be used only when acceleration is uniform. The correct equation is chosen by checking which quantities are given and which quantity is required. v = u + at; s = ut + 1/2 at²; v² = u² + 2as. Here u is initial velocity, v is final velocity, a is uniform acceleration, t is time, and s is displacement. A car starts from rest and accelerates uniformly at 3 m/s² for 4 s. Here u = 0, a = 3 m/s², t = 4 s. Displacement s = ut + 1/2 at² = 0 + 1/2 × 3 × 16 = 24 m. Typical questions ask for final velocity, displacement, acceleration, or time from given values, often with 'starts from rest' meaning u = 0. Using s = vt instead of s = ut + 1/2 at² in accelerated motion is wrong because velocity is changing.