Instantaneous velocity

Instantaneous velocity is the slope of the position–time graph — the limit of average velocity.

Instantaneous velocity0 min · Free lecture

In this lesson

  • Instantaneous velocity is the slope of the position–time graph — the limit of average velocity.

Your speedometer reads instantaneous velocity; a trip summary gives only averages.

v = lim(Δt→0) Δx/Δt = dx/dt. Geometrically, it is the slope of the tangent to the x–t curve at that instant.

If x(t) is given, differentiate; if a graph is given, read the tangent slope. Zero slope means instantaneously at rest.

v=lim⁡Δt→0ΔxΔt=dxdtv = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t} = \frac{dx}{dt}

Instantaneous velocity as a derivative

Worked example

The slope of a velocity–time graph gives:

  1. Slope = Δv/Δt = acceleration.

Answer: Acceleration

Transcript (0 min)
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Instantaneous velocity — FemtoLearn.
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Instantaneous velocity is the slope of the position–time graph — the limit of average velocity.
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Practice

Free · 4 questions with full solutions
  1. Q1 · MCQ · difficulty 2/5

    The slope of a velocity–time graph gives:

    • Displacement
    • Acceleration
    • Speed
    • Distance
  2. Q2 · 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.

  3. Q3 · 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
  4. Q4 · 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.