Equations of motion (constant acceleration)

The big three: v = u + at, s = ut + ½at², v² = u² + 2as — valid only for constant acceleration.

Equations of motion (constant acceleration)0 min · Free lecture

In this lesson

  • The big three: v = u + at, s = ut + ½at², v² = u² + 2as — valid only for constant acceleration.

Four quantities, three equations, one unknown: pick the equation with the three quantities you know.

With constant acceleration a, initial velocity u, final velocity v, displacement s and time t: v = u + at; s = ut + ½at²; v² = u² + 2as.

Strategy: list u, v, a, s, t — tick the ones you know and the one asked. The equation containing exactly those is yours. Signs: fix the positive direction first.

v=u+at,s=ut+12at2,v2=u2+2asv = u + at,\quad s = ut + \tfrac{1}{2}at^2,\quad v^2 = u^2 + 2as

The three kinematic equations

Worked example

A car starts from rest and accelerates at 2 m/s² for 5 s. Find its final velocity and displacement.

  1. u = 0, a = 2, t = 5.
  2. v = u + at = 0 + 2×5 = 10 m/s.
  3. s = ut + ½at² = 0 + ½×2×25 = 25 m.

Answer: v = 10 m/s; s = 25 m.

Using these equations when acceleration is NOT constant is the most common marks-loser in kinematics.
Transcript (0 min)
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Equations of motion (constant acceleration) — FemtoLearn.
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The big three: v = u + at, s = ut + ½at², v² = u² + 2as — valid only for constant acceleration.

Frequently asked

Are the equations valid for free fall?

Yes — with a = ±g and your chosen sign convention.

Printable notes (free)

Practice

Free · 4 questions with full solutions
  1. Q1 · Numerical · difficulty 1/5

    A body moving with initial velocity 16 m/s accelerates uniformly at 4 m/s². Find its velocity after 9 s.

  2. Q2 · Numerical · difficulty 2/5

    A body starts from rest and accelerates uniformly at 9.5 m/s². Find the displacement in the 8th second of its motion.

  3. Q3 · Numerical · difficulty 2/5

    The acceleration of a body starting from rest is a = 2 m/s² for 4 s, then zero for 2 s. Find its velocity at t = 6 s.

  4. Q4 · Numerical · difficulty 2/5

    A body starts from rest with a = 4 m/s². Find the displacement in the 5th second.