Position-time Graph – Complete Notes, Revision, Important Questions & Downloads
The position-time (x-t) graph is the first graphical representation of motion in NEET kinematics. One subtopic is covered: Graphical Representation and Interpretation. The key relationship is: slope of x-t graph = velocity = tan θ (where θ is the angle the tangent makes with the time axis). From this single principle, all common x-t graph shapes can be decoded: horizontal line (rest), straight line with positive slope (uniform positive velocity), curved line with increasing slope (positive acceleration), curved line with decreasing slope (negative acceleration, deceleration), and line returning toward origin (negative velocity, particle returning). NEET tests x-t graphs in two ways: (1) read the velocity from the slope; (2) identify which x-t graph matches a given description of motion.
NEET Weightage — Position-time Graph
Motion In One Dimension (Chapter 2)| NEET Year | Questions from this Topic | Bar | Marks |
|---|---|---|---|
| 2024 | 1 | 4 | |
| 2023 | 0 | 0 | |
| 2022 | 1 | 4 | |
| 2021 | 1 | 4 | |
| 2020 | 1 | 4 | |
| 2019 | 0 | 0 | |
| 6-Year Total (2019–2024) | 2–4 | 8–16 |
Impossible x-t graph: a vertical line (θ = 90°). This would mean the particle is at two different positions at the same time — physically impossible. NEET tests knowledge of this impossibility.
Straight x-t graphs that are parallel to each other: particles have the same velocity (same slope) but different positions — they never meet if running parallel to the time axis offset by a constant gap.
Exam Strategy — Position-time Graph in NEET
Read velocity from slope: velocity = tan θ The slope of the tangent to the x-t graph at any point gives the instantaneous velocity at that point. For a straight-line x-t graph: v = (x₂−x₁)/(t₂−t₁) = constant (uniform velocity). For a curved x-t graph: draw a tangent at the required point and measure its slope. θ is the angle the tangent makes with the positive time axis. v = tan θ.
Map graph shapes to motion types Horizontal line (θ=0°): v = 0 (body at rest). Straight positive slope: v = positive constant (uniform velocity). Straight negative slope: v = negative constant (returning to origin). Concave up curve (θ increasing): velocity increasing → positive acceleration. Concave down curve (θ decreasing): velocity decreasing → deceleration. Line crossing x-axis: particle passes through origin. Two x-t lines intersecting: particles at the same position at that time (not necessarily same velocity).
Identify steep, vertical, and multi-valued x-t graphs Steeper slope = larger |v|. A vertical line on an x-t graph is physically impossible (infinite velocity — particle in two places at same time: wait, no — vertical line means same t for multiple x values, which means infinite velocity OR that the graph is not a function). A graph that doubles back (x-t curve forming a loop, e.g., concave paths going backward) would have a region where the particle is at the same x at two different times — allowed physically only if x-axis is position and particle returns.
Download Study Notes — Position-time Graph
PDF · Cheat Sheet · MCQ Set · PYQSubtopics in Position-time Graph
2-Column TableRapid Revision — Position-time Graph
Concept → Trap → Example1) Graphical Representation and Interpretation
Slope = VelocitySlope of x-t graph (tangent) = instantaneous velocity = tan θ. Positive slope → positive velocity. Negative slope → negative velocity. Zero slope → at rest. Increasing θ → increasing velocity → positive acceleration. Decreasing θ → decreasing velocity → deceleration. Vertical line → impossible (infinite velocity).
- Straight-line x-t graph: θ = constant → v = constant → a = 0 (uniform velocity). Key: 'θ = constant so v = constant, a = 0 i.e., line with constant slope represents uniform velocity of the particle.'
- Curved x-t graph with increasing slope: particle's velocity is increasing with time — this is positive acceleration. The curve is concave upward (like a parabola opening upward for constant positive acceleration).
- Two x-t lines intersecting at a point: both particles are at the same position at that instant. Their velocities (slopes) may differ — they cross each other's positions but are not necessarily at the same velocity.
US Curriculum Gaps — Position-time Graph for NEET
US AP Physics students may find these specific aspects of x-t graph interpretation less familiar in NEET context.NEET uses angle θ notation for slope of x-t graph (not rise/run notation)
US AP Physics computes slopes using rise/run = Δx/Δt. NEET textbooks and resources often express the same quantity as v = tan θ, where θ is the angle the tangent (or the line) makes with the positive time axis. These are mathematically identical: tan θ = opposite/adjacent = Δx/Δt. However, NEET MCQs may use θ directly — 'the slope angle θ increases with time, what does this mean?' Students need to recognise tan θ as the velocity and an increasing θ as speeding up.
- tan θ = slope = Δx/Δt = velocity. If θ increases from 30° to 60°: velocity increases from tan 30° = 0.577 to tan 60° = 1.732 — positive acceleration.
- Critical special values: θ = 0° → tan 0° = 0 → at rest. θ = 45° → tan 45° = 1 m/s (if units are m/s). θ = 90° → tan 90° = ∞ → impossible for x-t graph.
- NEET phrasing: 'The angle that the position-time graph of a particle makes with the time axis is decreasing with time. What is the nature of acceleration?'
Identifying impossible x-t graphs is not explicitly tested in AP Physics but is testable in NEET
NEET tests whether a student can identify a physically impossible x-t graph. The most common impossible case is a vertical line (infinite slope, implying infinite velocity). Another impossible case is an x-t graph that goes backwards in time (physically impossible: time only moves forward). AP Physics 1 students learn to read slopes but are not typically asked to identify which of four x-t graphs is physically impossible.
- Impossible: vertical x-t line. Reason: slope = ∞ → infinite velocity — not physically realisable.
- Impossible: x-t graph that curves back toward the time axis and becomes tangent to it from above — this implies the particle was at two different positions at the same time instant.
- Ambiguous but not impossible: a U-shaped x-t curve (particle went forward then returned). This is physically possible — the particle is at the same position at two different times.
NEET-Style Practice Questions — Position-time Graph
4 NEET-style practice questionsPractice Problems — Position-time Graph
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Physics — Position-time Graph Revision Checklist
Use this section for quick chapter tracking before mocks, part tests, and final NEET revision.
Frequently Asked Questions — Position-time Graph
Notes · Downloads · Revision · Important QuestionsHow does the slope of a position-time graph give velocity?
What does a concave-up curve on an x-t graph mean?
What does a concave-down curve on an x-t graph mean?
If two x-t lines intersect, does that mean the particles collide?
What is the x-t graph for a freely falling body?
Can the x-t graph have a negative position on the x-axis?
How do I find when two particles A and B on the same x-t graph have equal velocities?
What is the physical meaning of the area under a position-time curve?
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