Motion in a Straight Line — Class XI Physics Notes | eduPhysics
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Class XI · Chapter 02

Motion in a Straight Line

The first real physics chapter: pinning down exactly what "speed," "velocity," and "acceleration" mean, and the equations that connect them for the simplest possible case — motion along a line.

● Easy ⏱ 22 min read 🎯 32 practice questions 📊 Not yet revised
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1Position, Path Length and Displacement

Describing motion starts with describing position — a location relative to a chosen reference point (origin) along a line.

Displacement
Δx = x₂ − x₁
Displacement is a vector — it can be positive, negative, or zero, and only cares about the start and end points, not the route taken between them.
Path Length vs. Displacement Path length (distance travelled) is a scalar — the total length actually covered, regardless of direction. Walk 5 m forward and 5 m back, and your displacement is zero, but your path length is 10 m. Path length is always greater than or equal to the magnitude of displacement; they're equal only for motion in a single, unchanging direction.

2Average Velocity and Average Speed

Average Velocity
vavg = Δx / Δt
Total displacement divided by total time — a vector, and it can be zero even if the object moved plenty (if it ends up back where it started).
Average Speed
Average speed = total path length / total time
A scalar, always ≥ the magnitude of average velocity over the same interval — equal only when motion never reverses direction.

3Instantaneous Velocity and Speed

Average velocity describes an entire interval, but motion often changes moment to moment. Instantaneous velocity is what a speedometer-like measurement gives you at one specific instant — the limit of average velocity as the time interval shrinks toward zero.

Instantaneous Velocity
v = dx / dt
Geometrically, this is the slope of the position-time graph at that exact instant. Instantaneous speed is simply the magnitude |v| — always non-negative.

4Acceleration

Acceleration measures how quickly velocity itself is changing — not just speeding up, but any change in velocity, including slowing down or changing direction.

Average and Instantaneous Acceleration
aavg = Δv / Δt, a = dv / dt = d²x / dt²
A negative acceleration doesn't automatically mean "slowing down" — it depends on the sign of velocity too. An object can speed up while its acceleration is negative, if it's moving in the negative direction.

5Position-Time and Velocity-Time Graphs

  • On a position-time graph, the slope at any point gives instantaneous velocity. A straight line means constant velocity; a curving line means the velocity is changing (i.e. there's acceleration).
  • On a velocity-time graph, the slope gives instantaneous acceleration, and — just as usefully — the area under the curve between two times gives the displacement over that interval.
Common Slip The area under a v-t graph gives displacement, not distance — if velocity goes negative (motion reverses), that portion of area counts negatively toward net displacement, even though the object was still covering ground (adding to path length).

6Kinematic Equations

For motion with constant acceleration only, three compact equations connect initial velocity u, final velocity v, acceleration a, displacement x, and time t.

Kinematic Equations
v = u + at    x = ut + ½at²    v² = u² + 2ax
Pick whichever equation already contains the variable you don't know and skips the one you don't need — this alone solves most straight-line motion problems directly, without needing calculus.
Displacement in the nth Second
sn = u + (a/2)(2n − 1)
Useful for "how far did it travel during the 5th second" style questions, rather than total distance up to that time.

7Relative Velocity

Velocity always depends on your frame of reference — "how fast" only makes sense relative to something. The velocity of object A as seen by an observer moving with object B is:

Relative Velocity
vAB = vA − vB
If two cars travel in the same direction, their relative velocity is smaller than either individual speed; if they move toward each other, relative velocity adds up — the reason head-on closing speeds feel so much faster.

Formula Summary

Displacement
Δx = x₂ − x₁
Average Velocity
v_avg = Δx/Δt
Instantaneous Velocity
v = dx/dt
Acceleration
a = dv/dt
First Equation
v = u + at
Second Equation
x = ut + ½at²
Third Equation
v² = u² + 2ax
nth Second
s_n = u + (a/2)(2n−1)
Relative Velocity
v_AB = v_A − v_B

Solved Examples

Example 1 · Kinematic Equations

A car starts from rest and accelerates uniformly at 2 m/s² for 10 s. Find its final velocity and the distance covered.

Solution: v = u + at = 0 + 2×10 = 20 m/s.

x = ut + ½at² = 0 + ½×2×(10)² = 100 m.

Example 2 · Relative Velocity

Two trains A and B move in the same direction at 72 km/h and 54 km/h. Find the velocity of A relative to B.

Solution: Convert to m/s: 72 km/h = 20 m/s, 54 km/h = 15 m/s.

vAB = vA − vB = 20 − 15 = 5 m/s, in the direction both trains are moving — that's the speed at which A appears to pull away from B, or B recedes when viewed from A.

Quick Check

1. If an object's displacement over some time interval is zero, its path length (distance travelled):
Must also be zero
✓ Can still be greater than zero (correct)
Must be negative
Equals the average velocity
2. The slope of a velocity-time graph gives:
Displacement
Average speed
✓ Acceleration (correct)
Path length
← Previous · Chapter 01

Units and Measurement

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Motion in a Plane

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