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# Displacement-time graphs

A displacement-time graph shows the time $t$ on the $x$-axis and the displacement $\vecphy{s}$ of an object on the $y$-axis. The object in question is assumed to undergo linear motion.

Negative $\vecphy{s}$ values imply that the object has moved past its starting point in the opposite direction.

The gradient of the graph is equal to the velocity at time $t$.

A straight line in the displacement-time graph indicates constant velocity. When the straight line is horizontal, $v=0 \text{ m/s}$. In other words, the object stands still.

• A - object travels at uniform speed of $2 \umps$.
• B - object is at rest $2 \um$ from origin.
• C - object travels at $-2 \umps$, passing origin on the way.
• D - object is at rest $-2 \um$ from origin.
• E - object travels at uniform speed of $2 \umps$, returning to origin.