The *instantaneous* *velocity* at time t is the *slope *of the *tangent line *drawn to the *position*-versus-*time *graph at that time.

The *instantaneous acceleration *at time t is the *slope *of the *tangent* drawn to the *velocity*-versus-*time* graph.

**Displacement from Velocity-Time Graphs**

time.

Given a *velocity**-*versus-*time* graph, the *displacement* during an interval between time *ti *and tf is the *area bounded by the velocity curve* and the two vertical lines *t = ti *and *t = tf*, as shown in the figure.

Given an *acceleration*-versus-*time* graph, the change in velocity between *t = ti *and *t = tf* is the *area bounded by the acceleration curve* and the vertical lines *t* = *ti *and *t *= *tf*.

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