NEET Physics · Kinematics
Motion Graphs
x–t · v–t · a–t
Master the relationship between position, velocity, and acceleration graphs — the most tested topic in NEET kinematics.
Section 1 of 5 · Foundations
What you'll learn in this tool
This interactive animation breaks motion graphs into three focused sections. By the end, you'll be able to look at any graph and instantly know what the other two look like — which is exactly what NEET asks.
Core slope rulesUnderstand why slope of x–t gives velocity and slope of v–t gives acceleration — with visual proof.
The derivative chainSee how x, v, and a are linked through differentiation (slope) and integration (area).
6 animated examplesWatch each graph type draw itself step-by-step, with explanations synced to the animation.
NEET traps highlightedCommon wrong answers and the reasoning behind them — flagged in every example.
x–t Position vs Time
v–t Velocity vs Time
a–t Acceleration vs Time
Position
x
metres (m)
slope →
⇌
← area
Velocity
v = dx/dt
m/s
slope →
⇌
← area
Acceleration
a = dv/dt
m/s²
Forward — differentiate
slope of x–t = v
The slope (gradient) at any point on the x–t graph gives the instantaneous velocity. Steeper slope = faster speed.
Forward — differentiate
slope of v–t = a
The slope at any point on the v–t graph gives the instantaneous acceleration. Flat v–t = zero acceleration.
Backward — integrate
area of v–t = Δx
Area under the v–t graph between two times gives the displacement in that interval. Can be negative (area below axis).
Backward — integrate
area of a–t = Δv
Area under the a–t graph gives the change in velocity in that interval. This is how impulse changes momentum.
Section 1 of 5
Section 2 of 5 · Forward Direction
Part A — Given x–t, derive v–t and a–t
You're given a position–time graph. Your job: figure out what the velocity–time and acceleration–time graphs look like. This tests whether you can read slope and curvature.
1
Pick an exampleClick any card in the row below the instructions — 6 different motion types are available.
2
Click ▶ AnimateWatch x–t draw first, then v–t appears as its slope result, then a–t as the slope of v–t.
3
Read the explanationSteps appear one by one below the graphs — each one matches a phase of the animation.
Choose an Example
—
—
x–t Graph (Given)
→
slope
v–t Graph (Derived)
→
slope
a–t Graph (Derived)
Step-by-step reasoning
NEET TIP—
Section 2 of 5
Section 3 of 5 · NEET Favourite Direction
Part B — Given v–t, derive a–t
NEET most frequently gives you a v–t graph and asks what the a–t graph looks like. The key skill: read each segment's slope and map it to a horizontal band in a–t. The example from your question (trapezoid v–t) is Example 01.
1
Pick a v–t shapeChoose from 4 classic shapes — triangle, trapezoid, flat line, and velocity reversal. Each maps to a distinct a–t pattern.
2
Click ▶ AnimateThe v–t graph draws first, then the a–t graph builds segment by segment — each step tied to one phase of the v–t shape.
3
Spot the NEET trapEvery example highlights a common wrong answer. The trap box appears after the animation completes.
Choose an Example
—
—
v–t Graph (Given)
a–t Graph (Derived)
Step-by-step derivation
NEET TIP—
Section 3 of 5
Section 4 of 5 · Slope Reading Drill
Part C — Given x–t, derive v–t
A focused drill on the most fundamental skill in motion graphs: reading the slope of a position–time graph and translating it into a velocity–time graph. Each example isolates one x–t shape so you can clearly see how it maps to v–t.
1
Pick an x–t shapeFour distinct shapes — straight line, parabola, peak curve (with sign change), and S-curve. Each produces a unique v–t pattern.
2
Click ▶ Animatex–t draws first, then v–t emerges as its slope. Watch how each change in x–t steepness maps directly onto the height of v–t.
3
Ask the slope questionAt each instant: is x–t getting steeper or flatter? Rising or falling? That answer IS the v–t value at that moment.
Choose an Example
—
—
x–t Graph (Given)
v–t Graph (Derived)
Step-by-step reasoning
NEET TIP—
Section 4 of 5
Section 5 of 5 · Revision Sheet
Quick Reference — Shape → Meaning
Every graph shape and what it means across all three graph types. Use this as your last-minute revision card before the exam. Print it, screenshot it, commit it to memory.
| Graph Shape / Feature | x–t meaning | v–t meaning | a–t meaning |
|---|---|---|---|
| Horizontal flat line | At rest (x = constant) | Constant velocity, a = 0 | Zero acceleration throughout |
| Straight line, +ve slope | Constant +ve velocity | Constant +ve acceleration | Constant +ve jerk (rare in NEET) |
| Straight line, −ve slope | Moving backwards (−v) | Decelerating (−a) | Constant −ve jerk |
| Concave up (∪ shape) | Velocity increasing (a > 0) | Acceleration increasing | Jerk > 0 |
| Concave down (∩ shape) | Velocity decreasing (a < 0) | Acceleration decreasing | Jerk < 0 |
| Slope = 0 at a point | v = 0 at that instant | a = 0 at that instant | — |
| Graph crosses x-axis | x = 0 (back at origin) | v = 0 (momentarily at rest) | a = 0 (no acceleration) |
| Area under curve | — (not standard) | = Displacement Δx | = Change in velocity Δv |
| Triangle shape | Parabolic motion (UAM) | Accelerate then decelerate | +a then −a (two steps) |
| Trapezoid shape | Accelerate, coast, decelerate | Accelerate, flat, decelerate | +a, 0, −a (three steps) |
| Abrupt jump / vertical | Physically impossible | Infinite acceleration (impulse) | Dirac spike (impulse) |
| v = 0 but slope ≠ 0 | — | Object momentarily at rest BUT still accelerating | a ≠ 0 at that point |
Common NEET Traps — Memorise These
TRAP 1v = 0 ≠ a = 0. When v–t crosses the x-axis, the object is momentarily at rest — but the slope of v–t is unchanged, so acceleration is still acting. Classic example: ball at peak of throw.
TRAP 2Straight x–t ≠ straight v–t. A straight x–t means constant v (a=0), not constant acceleration. A curved x–t means v is changing (a ≠ 0).
TRAP 3Negative displacement ≠ negative position. Area below the x-axis in v–t is negative displacement — the object moved backwards. But the final position could still be positive.
TRAP 4Trapezoid v–t → 3-step a–t. Each linear segment of v–t becomes a horizontal band in a–t. Vertical jumps in a–t occur wherever slope of v–t changes abruptly.
Section 5 of 5 · Complete!