Simulation · Physics · Class 11

Position, velocity and the graphs that record them

From the lesson Reading motion graphs in Motion in a Straight Line. Change the values and watch what happens.

The idea behind it

NCERT § "Acceleration"

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.

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