Schooling · Class 11 · Physics · Motion in a Straight Line · Chapter on a page
CBSE Class 11 · Physics · NCERT Physics Part-I
Motion in a Straight Line: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 27 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- Frame of reference
- Distance vs displacement
- Speed vs velocity
- Acceleration
- Uniform motion
- Uniformly accelerated motion
- Free fall
- Formulas and facts
- Displacement
- Average velocity
- Instantaneous velocity
- Average acceleration
- Instantaneous acceleration
- First kinematic equation
- Second kinematic equation
- Worked examples
- Finding displacement and distance
- Uniform acceleration on a straight…
- Free fall from a water tank
- Watch out for
- Treating distance and displacement…
- Forgetting signs when objects…
- Using kinematic equations when…
- Confusing the slope of an x–t graph…
- Dropping the factor 1/2 in x = ut +…
What this chapter is about
This chapter introduces kinematics — the study of motion without considering the forces that cause it. You focus entirely on objects moving along a straight path, which physicists call one-dimensional or rectilinear motion. Understanding this restricted case builds the vocabulary and mathematical tools you will need before tackling motion in two and three dimensions.
Key ideas
- Frame of reference: Motion is always described relative to a chosen origin and coordinate axis. An object at rest in one frame may be moving in another.
- Distance vs displacement: Distance is the total path length (always positive); displacement is the change in position with a direction (can be positive, negative or zero).
- Speed vs velocity: Speed is distance travelled per unit time (scalar); velocity is displacement per unit time (vector). Average speed can differ from the magnitude of average velocity.
- Acceleration: The rate of change of velocity. In straight-line motion, acceleration along the direction of velocity speeds the object up; acceleration opposite to velocity slows it down.
- Uniform motion: Velocity is constant, so acceleration is zero. The position–time graph is a straight line with slope equal to velocity.
- Uniformly accelerated motion: Acceleration is constant. Three kinematic equations relate initial velocity, final velocity, acceleration, displacement and time.
- Free fall: Near the Earth's surface an object falling under gravity alone has constant downward acceleration g ≈ 9.8 m/s². Air resistance is ignored at this level.
- Graphical interpretation: The slope of a position–time (x–t) graph gives velocity; the slope of a velocity–time (v–t) graph gives acceleration; the area under a v–t curve gives displacement.
Formulas and facts to remember
- Displacement: Δx = x₂ − x₁ (final position minus initial position, with sign).
- Average velocity: v_avg = Δx / Δt (displacement divided by time interval).
- Instantaneous velocity: v = dx/dt (the limit of Δx/Δt as Δt → 0).
- Average acceleration: a_avg = Δv / Δt.
- Instantaneous acceleration: a = dv/dt = d²x/dt².
- First kinematic equation (constant a): v = u + at, where u is initial velocity.
- Second kinematic equation: x = ut + (1/2)at², giving displacement in time t.
- Third kinematic equation: v² = u² + 2ax, linking velocities and displacement without time.
- Free-fall acceleration: g ≈ 9.8 m/s² downward near the Earth's surface.
Common mistakes
- Treating distance and displacement as the same → Remember displacement has direction; if you return to your starting point, displacement is zero even though distance is not.
- Forgetting signs when objects reverse direction → Choose a positive direction and keep acceleration negative if it opposes velocity.
- Using kinematic equations when acceleration is not constant → These formulas require constant acceleration; otherwise use calculus or graphs.
- Confusing the slope of an x–t graph with acceleration → Slope of x–t gives velocity; for acceleration, read the slope of the v–t graph.
- Dropping the factor 1/2 in x = ut + (1/2)at² → Derive it once by integration or area method and the factor will stick.
Quick revision
- Displacement = change in position (vector); distance = path length (scalar).
- Velocity = dx/dt; acceleration = dv/dt.
- Three constant-acceleration equations: v = u + at, x = ut + (1/2)at², v² = u² + 2ax.
- Slope of x–t graph → velocity; slope of v–t graph → acceleration; area under v–t graph → displacement.
- Free fall near Earth: a = g ≈ 9.8 m/s² downward, with air resistance ignored.