Average velocity over symmetric intervals

Under constant acceleration, the average velocity over any interval equals the velocity at the midpoint in time.

Average velocity over symmetric intervals0 min · Free lecture

In this lesson

  • Under constant acceleration, the average velocity over any interval equals the velocity at the midpoint in time.

The average of the first and last velocities is the velocity in the middle — exactly.

For constant a, v_avg = (u + v)/2 = velocity at the mid-instant. Also, displacement in equal time intervals increases by aT² each step (Galileo's odd-number rule for starting from rest).

These shortcuts turn many JEE questions into mental arithmetic.

vavg=u+v2v_{avg} = \frac{u+v}{2}

Average velocity as the mid-value

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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Average velocity over symmetric intervals — FemtoLearn.
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Under constant acceleration, the average velocity over any interval equals the velocity at the midpoint in time.
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 · 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