C
CraftExam
medium difficulty7 min

Acceleration

Acceleration is the rate of change of velocity with time. It tells how quickly velocity changes in magnitude or direction.

In one line: Acceleration checks change in velocity, not just fast motion.

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Understand it

Acceleration can be positive, negative, or zero depending on how velocity changes. If velocity increases uniformly, acceleration is uniform and positive in the chosen direction. If velocity decreases, acceleration may be negative, often called retardation in school-level problems.

Example

A scooter increasing its velocity from 5 m/s to 15 m/s in 5 s has acceleration (15 - 5)/5 = 2 m/s².

Rule to remember

Acceleration, a = (v - u) / t, where u is initial velocity, v is final velocity, and t is time.

SI unit is m/s².

See it worked out

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

Worked example

A car slows from 20 m/s to 8 m/s in 4 s.

  1. 1a = (8 - 20)/4 = -12/4 = -3 m/s².
  2. 2The negative sign shows velocity is decreasing in the chosen positive direction.

Method you can reuse

  1. 1Identify u, v, and t.
  2. 2Keep units consistent.
  3. 3Substitute in a = (v - u)/t.
  4. 4Interpret the sign of acceleration according to the chosen direction.

Visual tip

A velocity arrow diagram can show increasing, decreasing, or changing direction of velocity.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Can an object have acceleration when its speed remains constant?

Think first, then show answer
Yes, an object can have acceleration with constant speed if its direction changes, because velocity depends on both speed and direction.

Common wrong answer

Writing +3 m/s² for a slowing car without explaining direction is usually wrong because the velocity has decreased.

Don't mix this up

Students often say acceleration means only speeding up, but change in direction or slowing down also involves acceleration.

Exam tip

Use final velocity minus initial velocity, not initial minus final, unless the sign convention demands it.

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

Numericals may ask for acceleration, retardation, final velocity, or time using a = (v - u)/t.
  1. 1

    Enough for 1 mark

    Acceleration is the rate of change of velocity with time. It tells how quickly velocity changes in magnitude or direction.

  2. 2

    Add for 2 marks

    Example: A scooter increasing its velocity from 5 m/s to 15 m/s in 5 s has acceleration (15 - 5)/5 = 2 m/s².

  3. 3

    Add for 3 marks

    Acceleration can be positive, negative, or zero depending on how velocity changes.

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