Reading motion graphs

x-t graph: slope gives velocity. v-t graph: slope gives acceleration and area gives displacement. a-t graph: area gives change in velocity.

To find distance from a v-t graph, add the magnitudes of the areas above and below the time axis; to find displacement, add them with their signs.

A point where the v-t graph crosses the time axis is where the body momentarily stops and reverses direction.

An x-t graph can never show two positions at the same instant, and a real v-t graph cannot jump suddenly, since that would need infinite acceleration.

In NCERT's idealised graphs the sharp corners (instant changes in velocity) are a simplification; real motion rounds them off.

When x is a polynomial in t, differentiate once for v and twice for a; if a depends on t, the kinematic equations of constant acceleration do not apply.