Motion in a Straight Line — Physics Class 11 Notes (CBSE & HBSE)
Free NCERT Physics notes for Motion in a Straight Line (Class 11) on Siksha Sarovar, aligned to CBSE and Haryana Board (HBSE). This chapter is broken into 3 topics with clear explanations, formulas, solved examples and board-pattern practice — free to read, no sign-up required.
Board exam focus — Motion in a Straight Line (CBSE & HBSE)
This chapter introduces kinematics — the description of motion without asking about its cause. Confining ourselves to one dimension, we define distance, displacement, speed, velocity and acceleration, learn to read position-time and velocity-time graphs, derive the three equations of uniformly accelerated motion, and handle relative velocity in 1D. It is a high-yield numerical chapter in both CBSE and HBSE.
Distance, Displacement, Speed, Velocity and Acceleration
Frame of Reference and Position
To describe motion we need a reference point (origin) and a frame of reference. In 1D, position is given by a single coordinate x along a chosen axis. A particle is treated as a point object when its size is small compared with the distance it moves.
Distance vs Displacement
| Quantity | Definition | Type |
|---|---|---|
| Distance (path length) | total length of path travelled | scalar, always >= 0 |
| Displacement | change in position, delta x = x2 - x1 | vector, can be +, - or 0 |
Key fact: |displacement| <= distance. They are equal only for motion along a straight line without reversing direction.
Speed and Velocity
- Average speed = total distance / total time.
- Average velocity = displacement / time = (x2 - x1)/(t2 - t1).
- Instantaneous velocity v = dx/dt (slope of the x-t graph).
- Instantaneous speed = magnitude of instantaneous velocity.
Acceleration
Acceleration is the rate of change of velocity:
- Average acceleration a_avg = (v2 - v1)/(t2 - t1) = delta v / delta t.
- Instantaneous acceleration a = dv/dt = d^2x/dt^2.
Uniform acceleration means a is constant in magnitude and direction.
Sign Conventions
- Choose a positive direction for the axis.
- Velocity is positive when motion is along +x, negative against it.
- Retardation (deceleration) occurs when velocity and acceleration have opposite signs — the body slows down.
CBSE/HBSE trap: A body can have zero velocity but non-zero acceleration — e.g. a ball at the top of its vertical throw (v = 0, a = g downward).
Motion Graphs: Position-Time and Velocity-Time
The Position-Time (x-t) Graph
A graph of position x against time t reveals the nature of motion through its slope, because slope = dx/dt = velocity.
| x-t graph shape | Interpretation |
|---|---|
| Horizontal line | object at rest (v = 0) |
| Straight line with slope | uniform velocity |
| Curve bending upward | increasing velocity (acceleration) |
| Curve bending downward | decreasing velocity (retardation) |
The Velocity-Time (v-t) Graph
For a v-t graph, two geometric facts are central:
- Slope of v-t graph = acceleration (a = dv/dt).
- Area under v-t graph = displacement.
| v-t graph shape | Interpretation |
|---|---|
| Horizontal line | uniform velocity, zero acceleration |
| Straight inclined line | uniform acceleration |
| Line crossing time axis | velocity reverses direction |
Reading Displacement from a v-t Graph
For uniformly accelerated motion, the v-t graph is a straight line. The area under it (a trapezium) gives displacement:
s = (1/2)(u + v) t — the average-velocity form, where u and v are initial and final velocities.
For a velocity that goes positive then negative, areas below the time axis are negative; the net area equals displacement, while the total magnitude of areas equals distance.
Graphs in Words: Free Fall
For a ball dropped from rest:
- x-t graph is a downward-opening parabola (x = (1/2)g t^2).
- v-t graph is a straight line through the origin with slope g.
- a-t graph is a horizontal line at a = g.
CBSE/HBSE trap: The x-t graph can never be a vertical line — that would mean the object is at many positions at one instant (infinite velocity), which is impossible.
Equations of Uniformly Accelerated Motion and Relative Velocity
The Three Kinematic Equations
For motion with constant acceleration a, initial velocity u, final velocity v after time t, and displacement s:
- v = u + a t
- s = u t + (1/2) a t^2
- v^2 = u^2 + 2 a s
A useful fourth relation gives the displacement in the nth second:
s_n = u + (a/2)(2n - 1)
Quick Derivation (from v-t graph)
- Equation 1 comes directly from a = (v - u)/t.
- Equation 2 is the area under the v-t line: s = u t + (1/2) a t^2.
- Equation 3 is obtained by eliminating t between equations 1 and 2.
Motion Under Gravity
For vertical motion, replace a by g = 9.8 m/s^2 (often 10 m/s^2 in problems). Take a sign convention:
- Throwing up: a = -g (if up is positive).
- Dropping: u = 0, a = +g (if down is positive).
Relative Velocity in 1D
The relative velocity of object A with respect to object B is:
v_AB = v_A - v_B
- If both move in the same direction, subtract magnitudes.
- If they move in opposite directions, add magnitudes (because one velocity is negative).
| Situation | Relative velocity magnitude | ||
|---|---|---|---|
| Same direction | v_A - v_B | ||
| Opposite directions | v_A + v_B |
CBSE/HBSE trap: Always fix one positive direction before applying v_AB = v_A - v_B; mixing signs is the most common error in train/overtaking problems.
Frequently asked questions
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Do these notes follow CBSE and HBSE?
Yes. The Motion in a Straight Line notes are NCERT-aligned and include guidance for both CBSE and Haryana Board (HBSE), with important questions and MCQs for revision.
What does the Motion in a Straight Line chapter cover?
Concept explanations, key formulas and definitions, fully solved examples and board-pattern practice questions for Motion in a Straight Line.