Displacement in the nth second

Distance covered in the nth second: sₙ = u + a(n − ½) — a favourite one-liner.

Displacement in the nth second0 min · Free lecture

In this lesson

  • Distance covered in the nth second: sₙ = u + a(n − ½) — a favourite one-liner.

The 5th second is the interval from t = 4 s to t = 5 s — one second wide, not five.

Displacement during the nth second = displacement in n seconds − displacement in (n−1) seconds.

sₙ = [un + ½an²] − [u(n−1) + ½a(n−1)²] = u + a(n − ½). Works for any constant acceleration, including free fall with signs.

sn=u+a(n−12)s_n = u + a\left(n - \tfrac{1}{2}\right)

Displacement in the nth second

Worked example

A body starts from rest and covers 18 m in the 5th second. Find its acceleration.

  1. sₙ = u + a(n − ½) with u = 0, n = 5: 18 = a(5 − ½) = 4.5a.
  2. a = 18/4.5 = 4 m/s².

Answer: a = 4 m/s².

Transcript (0 min)
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Displacement in the nth second — FemtoLearn.
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Distance covered in the nth second: sₙ = u + a(n − ½) — a favourite one-liner.
Printable notes (free)

Practice

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

    A body starts from rest and accelerates uniformly at 9.5 m/s². Find the displacement in the 8th second of its motion.

  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.