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Motion in a Straight Line

NCERT Class 11 Physics Chapter 2

Motion in a Straight Line for Class 11 Physics, JEE and NEET: displacement, velocity, acceleration, motion graphs, equations of motion, relative velocity.

5 topics Updated 8 Nov 2026

For: Class 11, JEE and NEET, unless a topic says otherwise

In the syllabus: JEE Class 11 syllabus, NEET Class 11 syllabus

With your textbook

NCERT Physics Part I (Class 11), Chapter 2 “Motion in a Straight Line”, reprint 2026-27.

Open the official NCERT chapter (PDF, 1.4 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Frame of reference, position and displacement

    Path length, average velocity vs average speed and x-t graphs, with 5 solved examples.

    JEE and NEET only 15 min read 5 solved examples 6 practice questions

  2. Velocity and speed

    v = dx/dt as a limit, the slope of the x-t graph and speed vs velocity, with solved examples.

    NCERT Section 2.2 13 min read 5 solved examples 6 practice questions

  3. Acceleration

    Formula, unit, negative acceleration, v-t graphs and the area under them, with 5 solved examples.

    NCERT Section 2.3 16 min read 5 solved examples 6 practice questions

  4. Equations of motion for uniform acceleration

    v = v + at, x = vt + ½at, v = v + 2ax, derived by graph and calculus, free fall, stopping distance.

    NCERT Section 2.4 18 min read 6 solved examples 6 practice questions

  5. Relative velocity

    vAB = vA − vB in one and two dimensions, overtaking, rain-umbrella and river boat problems, with examples.

    JEE and NEET only 16 min read 6 solved examples 6 practice questions

Key formulas in this chapter

Frame of reference and displacement

  • Δx = x − x
  • v̄ = Δx/Δt = (x − x)/(t − t)
  • average speed = path length/time interval
  • average speed ≥ |v̄|
  • equal distances at v and v: average speed = 2vv/(v + v)

Velocity and speed

  • v = lim(Δt→0) Δx/Δt
  • v = dx/dt (slope of the tangent to the x-t graph)
  • speed = |v|
  • d(t)/dt = n t
  • x = a + bt: v = 2bt

Acceleration

  • ā = (v − v)/(t − t) = Δv/Δt
  • a = dv/dt
  • a = dx/dt
  • constant a: v = v + at
  • displacement = net area under the v-t graph; distance = total area
  • a = v dv/dx
  • area under the a-t graph = change of velocity

Equations of motion

  • v = v + at
  • x = vt + ½at
  • v = v + 2ax
  • x = ½(v + v)t
  • starting at x: replace x by x − x
  • free fall, upwards positive: a = −g
  • nth second: x(n) − x(n − 1) = v + a(n − ½)
  • ds = v0^2/(2|a|); tr = √(2d/g)

Relative velocity

  • vAB = vA − vB
  • vBA = −vAB
  • vAB^2 = vA^2 + vB^2 − 2vA vB cos θ
  • rain: tan α = vm/vr
  • river, shortest time: t = d/u; drift = vd/u
  • river, shortest path: sin θ = v/u; t = d/√(u − v)
  • river, least drift (u < v): sin θ = u/v; drift = d√(v − u)/u

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