Velocity-time Graph – Complete Notes, Revision, Important Questions & Downloads
The velocity-time (v-t) graph is the most powerful graphical tool in 1D kinematics for NEET — it encodes both acceleration (from slope) and displacement (from area under the curve) simultaneously. Three subtopics are covered: Graphical Representation (what v-t graphs look like), Calculation of Acceleration from v-t Graph (slope = acceleration = tan θ), and Interpretation of v-t Graphs (area above t-axis = positive displacement; area below = negative displacement; total area = total distance). NEET tests v-t graphs in three ways: (1) find acceleration from slope; (2) find displacement from area under curve; (3) identify the type of motion from the graph shape. The v-t graph area-displacement relationship is among the most tested graphical skills in NEET Chapter 2.
NEET Weightage — Velocity-time Graph
Motion In One Dimension (Chapter 2)| NEET Year | Questions from this Topic | Bar | Marks |
|---|---|---|---|
| 2024 | 1 | 4 | |
| 2023 | 1 | 4 | |
| 2022 | 1 | 4 | |
| 2021 | 1 | 4 | |
| 2020 | 1 | 4 | |
| 2019 | 1 | 4 | |
| 6-Year Total (2019–2024) | 3–6 | 12–24 |
Area under v-t graph: area between the v-t curve and the time axis = displacement (signed). Area above t-axis is positive displacement; area below is negative displacement. Total distance = sum of absolute areas of all segments.
A v-t graph crossing the time axis (v = 0) means the particle momentarily stopped. The areas before and after this crossing have opposite signs — displacement in one direction, then the other.
Exam Strategy — Velocity-time Graph in NEET
Read acceleration from slope: acceleration = tan θ For a straight-line v-t segment: a = (v₂−v₁)/(t₂−t₁) = constant (uniform acceleration). For a curved v-t line: instantaneous acceleration = slope of tangent at that point. Positive slope → positive acceleration. Negative slope → negative acceleration (deceleration for v > 0). Horizontal line (θ = 0°) → a = 0 → uniform velocity.
Compute displacement from area: displacement = signed area under v-t curve Identify all closed regions between the v-t curve and the time axis. Regions above the t-axis (v > 0): contribute positive displacement (+area). Regions below the t-axis (v < 0): contribute negative displacement (−area). Total displacement = sum of all signed areas. Total distance = sum of absolute values of all areas. For NEET: identify the geometric shape (triangle, rectangle, trapezoid), compute its area using the formula, and apply the sign from its position relative to the t-axis.
Identify standard graph shapes and motion types Horizontal line (v > 0): uniform velocity, a = 0. Rising straight line: uniform positive acceleration. Falling straight line: uniform negative acceleration or deceleration. Line crossing the t-axis: particle reverses direction at the crossing point. Curved line (concave): non-uniform acceleration. Parallel segments at different v levels may indicate segments of constant velocity separated by instantaneous velocity changes.
Download Study Notes — Velocity-time Graph
PDF · Cheat Sheet · MCQ Set · PYQSubtopics in Velocity-time Graph
2-Column TableRapid Revision — Velocity-time Graph
Concept → Trap → Example1) Graphical Representation
v on y-axis, t on x-axisVelocity-time graph: v on y-axis, t on x-axis. The shape of the v-t graph reveals both the acceleration (from slope) and the displacement (from area). Standard shapes: horizontal line = constant v, a = 0; rising line = positive acceleration; falling line = negative acceleration; line crossing t-axis = particle reverses direction.
- The graph plots velocity (not speed) on the y-axis — it can have negative y-values when the particle moves in the negative direction.
- A v-t graph line crossing the t-axis (v passing through 0): particle instantaneously stops and reverses direction at that time.
- The steeper the slope, the larger the acceleration magnitude. Parallel v-t lines have the same acceleration (same slope).
2) Calculation of Acceleration from v-t Graph
Slope of v-t = AccelerationAcceleration = slope of v-t graph = tan θ = (v₂−v₁)/(t₂−t₁) = Δv/Δt. For straight-line v-t graphs: uniform acceleration (constant slope). For curved v-t graphs: non-uniform acceleration; instantaneous a = slope of tangent at that point. Key NCERT: 'It is clear that slope of tangent on velocity-time graph represents the acceleration of the particle.'
- Zero slope (horizontal v-t line): θ = 0°, a = 0, v = constant. Meaning: particle moves at constant velocity.
- Negative slope: v decreasing with time. If v > 0 and slope < 0: decelerating. If v < 0 and slope < 0: accelerating in negative direction.
- The sign of acceleration on v-t graph: positive slope → positive a. Negative slope → negative a. The sign of velocity on v-t graph: v above t-axis (y > 0) → positive direction. v below t-axis (y < 0) → negative direction.
3) Interpretation of v-t Graphs
Area = Displacement; |Area| = DistanceThe area enclosed between the v-t curve and the time axis = displacement. Above t-axis: positive displacement. Below t-axis: negative displacement. Total displacement = algebraic sum of all signed areas. Total distance = sum of absolute values of all areas.
- NCERT verbatim: 'The area covered between the velocity time graph and time axis gives the displacement and distance travelled by the body for a given time interval.'
- Area geometry: triangular v-t region = ½ × base × height. Rectangular region = base × height. Trapezoidal region = ½ × (v₁+v₂) × Δt. Use these formulas when computing displacement from v-t graphs without integration.
- Special check: if total displacement required for a full journey and the v-t graph crosses the t-axis, split the area into regions above and below the axis, compute each separately, then sum with signs for displacement or sum absolute values for distance.
US Curriculum Gaps — Velocity-time Graph for NEET
US AP Physics students may find these specific aspects of v-t graph interpretation less thoroughly drilled for NEET.Signed area interpretation (positive above, negative below t-axis) is not always explicitly emphasised in US AP Physics 1
US AP Physics 1 teaches displacement = area under v-t graph, but may not drill the signed area distinction (above t-axis = positive displacement, below = negative displacement) with the same frequency as NEET. NEET problems routinely give a v-t graph that crosses the t-axis and require separate computation of displacement and distance — a process that requires computing two areas with opposite signs.
- Displacement = algebraic sum of areas (areas above t-axis positive, below negative).
- Distance = sum of absolute values of all areas (no sign).
- NEET trap: summing all areas algebraically gives displacement, but the student may be asked for distance — which requires treating all areas as positive.
Trapezoidal area for constant-acceleration v-t graphs is not always practised in US introductory courses
For a particle with initial velocity u, final velocity v, over time t: the v-t graph is a trapezoid. Displacement = ½(u+v)t — this is the trapezoidal area formula applied to kinematics. US AP Physics 1 derives this formula algebraically, but NEET tests it graphically — students must recognise the trapezoid, apply ½(b₁+b₂)h, and get the displacement directly from the graph geometry.
- Trapezoid area = ½ × (top base v + bottom base u) × height t = ½(u+v)t — same as the kinematic formula for displacement under constant acceleration.
- On a NEET v-t graph, the trapezoidal area below the slanted line and above the t-axis IS the displacement— computed geometrically.
- Practise: given a v-t graph with v₁ at t₁ and v₂ at t₂ (straight-line segment), area of trapezoid = ½(v₁+v₂)(t₂−t₁).
NEET-Style Practice Questions — Velocity-time Graph
4 NEET-style practice questionsPractice Problems — Velocity-time Graph
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Physics — Velocity-time Graph Revision Checklist
Use this section for quick chapter tracking before mocks, part tests, and final NEET revision.
Frequently Asked Questions — Velocity-time Graph
Notes · Downloads · Revision · Important QuestionsWhy does the area under the v-t graph equal displacement?
How do I calculate the area under a v-t graph without calculus?
What is the difference between distance and displacement on a v-t graph?
What does it mean when a v-t graph crosses the time axis?
Why is the slope of the v-t graph equal to acceleration?
What does a negatively sloped v-t graph line that is entirely below the time axis indicate?
If the v-t graph is a curve (not straight), how do I find the instantaneous acceleration at a specific point?
How is the v-t graph related to the x-t graph?
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