Check us out at http://www.tutorvista.com The slope of the line of a speed-versus-time graph will give you acceleration. Remember that acceleration may be positive or negative, and in some cases, acceleration may be positive when speed remains the same. If the speed-time curve is linear or piecewise linear, acceleration is, as stated above, merely the slope of the line segment. If, however, the graph is a smooth curve, then changing acceleration is represented. In other words, the rate of change of velocity -- delta-V over delta-T -- is not a constant. In that case, the slope of the line segment tangent to the curve at any given point is the acceleration at that point. If acceleration is non-zero, there must be a change in velocity. That is, after all, the definition of acceleration. Certainly, it is possible for acceleration to be positive while velocity is negative and vice versa, but a constant speed -- represented by a graph horizontal to the time axis -- implies zero acceleration.
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