Speed vs velocity

Speed is how fast (scalar); velocity is how fast and in which direction (vector).

Speed vs velocity0 min · Free lecture

In this lesson

  • Speed is how fast (scalar); velocity is how fast and in which direction (vector).

A car at 60 km/h around a curve has constant speed but changing velocity — direction matters.

Average speed = total distance / total time. Average velocity = displacement / time — a signed vector. Instantaneous values come from derivatives: v = dx/dt.

On a round trip, average velocity is zero but average speed is not. Exam setters love this distinction.

vavg=ΔxΔt,v=dxdtv_{avg} = \frac{\Delta x}{\Delta t}, \quad v = \frac{dx}{dt}

Average and instantaneous velocity

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

Transcript (0 min)
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Speed vs velocity — FemtoLearn.
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Speed is how fast (scalar); velocity is how fast and in which direction (vector).

Frequently asked

Can average speed equal average velocity?

Only for straight-line motion in one direction.

Printable notes (free)

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 · MCQ · difficulty 2/5

    The slope of a velocity–time graph gives:

    • Displacement
    • Acceleration
    • Speed
    • Distance
  4. Q4 · 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.