# Interpreting Motion Graphs > Motion graph interpretation for NEET Physics: slope and area rules for x-t and v-t graphs, standard shapes, and quick numerical tricks. - Canonical URL: https://prepelephant.com/topics/neet-ug/physics/motion-graphs-interpretation-neet - Exam / course: NEET-UG · Subject: Physics - Publisher: PrepElephant (https://prepelephant.com) — Prepared and reviewed by the PrepElephant Academic Review Team - First published: 2026-10-02 - Last updated: 2026-10-02 - How to cite: "Interpreting Motion Graphs", PrepElephant, https://prepelephant.com/topics/neet-ug/physics/motion-graphs-interpretation-neet ## Direct answer A position-time (x-t) graph encodes velocity as its slope: a flat line means rest, a straight sloping line means uniform velocity (v = Δx/Δt), and a curved line means accelerated motion, with the curvature's sign giving the direction of acceleration. A velocity-time (v-t) graph is richer — its slope gives acceleration (a = Δv/Δt) and the area under it gives displacement, taken negative where the curve dips below the time axis. An acceleration-time graph gives change in velocity as its area. Most NEET questions on this topic are exercises in reading these three quantities off a sketch, so the slope-area rules, applied with sign discipline, settle nearly every question in under a minute. ## What you must remember - **Slope rules:** slope of x-t = velocity; slope of v-t = acceleration; slope of a-t is not a standard quantity (its area is, and equals Δv). - **Area rules:** area under v-t = displacement (not distance — parts below the axis subtract); area under a-t = change in velocity Δv. - **Shape dictionary:** uniformly accelerated motion gives a parabola in x-t (opening along the acceleration direction), a straight inclined line in v-t, and a horizontal line in a-t. - **Reversal condition:** a body reverses direction only where v changes sign, i.e. where the v-t curve crosses the time axis or the x-t curve has a peak (zero slope) — never where a = 0 momentarily by itself. - **Average versus instantaneous:** the chord slope of an x-t graph between two points is average velocity; the tangent slope at a point is instantaneous velocity. NEET loves asking which is which on a curved x-t sketch. - **Standard value hook:** with g = 9.8 m/s^2 (NCERT convention; take 10 only if the paper gifts it), a free-fall v-t graph has slope 9.8 downward, and the area after t seconds works out to 4.9 t^2 metres of fall. - **Distance trap:** for a v-t graph that goes positive then negative with equal areas, net displacement is zero but the distance travelled is twice one area — read the question's last word carefully. ## Walking through a typical NEET sketch Suppose a v-t graph rises linearly from 0 to 20 m/s in 4 s, stays at 20 m/s for 4 s, then falls linearly to −10 m/s over the next 6 s. The three slopes give the accelerations: 20/4 = 5 m/s^2, then 0, then (−10 − 20)/6 = −5 m/s^2. For displacement, add the areas by inspection: a triangle of base 4 s and height 20 (40 m), a rectangle 4 × 20 (80 m), then a trapezium from t = 8 s to 14 s — the part above the axis is 20 × 4 × ½ = 40 m, and the triangle below the axis from t = 12 s to 14 s is ½ × 2 × 10 = 10 m with a negative sign. Total displacement = 40 + 80 + 40 − 10 = 150 m, while distance = 160 m. Notice how the zero-crossing at t = 12 s is the pivot: that is where the body stops and turns back, and every quantity after it flips sign. Working a full graph this way once is worth memorising ten formulas, because the exam rarely deviates from this triangle-rectangle-trapezium toolkit. ## How the exam frames graphs The recurring trap is graphical language that sounds precise but is not: "the slope of the graph is negative" is meaningless until you name which graph — negative v-t slope means retardation only while velocity is positive, and acceleration (not retardation) if velocity is already negative. A second favourite asks for the point of maximum speed on a curved x-t graph; students point to the steepest visible segment, which is right, but then misidentify it because the curve keeps steepening beyond the drawn window. NCERT Class 11, Chapter 3 builds the whole discussion around three named examples — a car at rest, one at uniform velocity, one accelerating — and NEET options are frequently the same three shapes shuffled, so anchor your answers to that NCERT trio rather than to exotic curves. ## Frequently asked questions ### What does the area under a velocity-time graph represent? It represents displacement; the portions below the time axis contribute negatively, so the total area with signs gives displacement while the sum of magnitudes gives distance travelled. ### When is a position-time graph a straight line? Only for rest (horizontal) or uniform velocity (inclined); any acceleration, constant or changing, bends the x-t graph, becoming a parabola when acceleration is uniform. ### How do you find where a body reverses its direction from a graph? Locate the instant velocity changes sign — the v-t curve crossing the time axis, equivalently a maximum or minimum (zero slope) point on the x-t curve. ### Can a body have zero velocity yet non-zero acceleration? Yes: at the topmost point of vertical throw or at the turning point of an oscillation, velocity is momentarily zero while acceleration remains 9.8 m/s^2 or a = −ω^2 x respectively. ### What is the difference between average and instantaneous velocity on a graph? Average velocity is the slope of the chord joining two points on the x-t graph; instantaneous velocity is the slope of the tangent at a single point, and the two coincide only for straight-line (uniform velocity) graphs.