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
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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