Acceleration: the basics

Acceleration is the rate of change of velocity — it can slow you down, speed you up, or just turn you.

Acceleration: the basics0 min · Free lecture

In this lesson

  • Acceleration is the rate of change of velocity — it can slow you down, speed you up, or just turn you.

Braking is acceleration too: negative in your direction of motion, but acceleration nonetheless.

a = dv/dt = d²x/dt². Acceleration is a vector; its direction is the direction of the CHANGE in velocity, not necessarily of motion.

Constant acceleration is the workhorse of JEE kinematics: the three equations of motion apply only then.

a=dvdt=d2xdt2a = \frac{dv}{dt} = \frac{d^2 x}{dt^2}

Acceleration as derivatives of velocity and position

Worked example

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.

  1. Area under the a–t graph = change in velocity.
  2. Area = 2 m/s² × 4 s = 8 m/s (the last 2 s add nothing).

Answer: 8

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Acceleration: the basics — FemtoLearn.
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Acceleration is the rate of change of velocity — it can slow you down, speed you up, or just turn you.
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Practice

Free · 4 questions with full solutions
  1. Q1 · 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.

  2. Q2 · MCQ · difficulty 2/5

    A particle moves with constant velocity. Which a–t graph describes it?

    • A horizontal line at a = 0
    • A horizontal line at a = 2 m/s²
    • A straight line through the origin
    • A parabola
  3. Q3 · Numerical · difficulty 2/5

    A body moves with v = 10 m/s for 3 s, then v = 5 m/s for 2 s in the same direction. Find the total distance.

  4. Q4 · MCQ · difficulty 2/5

    The slope of a velocity–time graph gives:

    • Displacement
    • Acceleration
    • Speed
    • Distance