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medium difficulty8 min

Kinematic Equations of Motion

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

In one line: Given, asked, formula, substitute, unit.

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Understand it

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.

Example

If a scooter starts from rest and accelerates at 2 m/s² for 5 s, v = u + at = 0 + 2 × 5 = 10 m/s.

Rule to remember

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.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A car starts from rest and accelerates uniformly at 3 m/s² for 4 s.

  1. 1Here u = 0, a = 3 m/s², t = 4 s.
  2. 2Displacement s = ut + 1/2 at² = 0 + 1/2 × 3 × 16 = 24 m.

Method you can reuse

  1. 1List given values with units.
  2. 2Convert units if needed.
  3. 3Identify the unknown.
  4. 4Choose the equation that contains the given values and the unknown.
  5. 5Substitute carefully and write the final unit.

Visual tip

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.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

When can the three equations of motion be used directly?

Think first, then show answer
They can be used directly when the object moves with uniform acceleration and the given quantities match one of the standard equations.

Common wrong answer

Using s = vt instead of s = ut + 1/2 at² in accelerated motion.

Why it loses marks: Velocity is changing.

Don't mix this up

Students often use these equations even when acceleration is not uniform, or they choose an equation containing an unknown that is not needed.

Exam tip

Write u, v, a, t, and s before selecting the formula; this prevents most substitution mistakes.

Kinematic Equations of Motion diagram

Open full screen to read every label clearly.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Typical questions ask for final velocity, displacement, acceleration, or time from given values, often with 'starts from rest' meaning u = 0.
  1. 1

    Enough for 1 mark

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

  2. 2

    Add for 2 marks

    Example: If a scooter starts from rest and accelerates at 2 m/s² for 5 s, v = u + at = 0 + 2 × 5 = 10 m/s.

  3. 3

    Add for 3 marks

    The three common equations are v = u + at, s = ut + 1/2 at², and v² = u² + 2as.

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