Steps to determining v vs. t curve from s vs. t curve (1)draw a set of axes (v vs t) directly under the s vs. t curve (2)locate all minimums, maximums, asymptotes, and inflection points (3)plot zero value points for each corresponding min, max or asym (4) plot mins or maxes for each inflection point

negative slope start negative but get closer to zero but flattening out

minimum = zero slope must cross time axis (i.e. v=0)

positive slope but becoming steeper Start at zero and increase

positive slope but becoming steeper start out flat slope stops becoming steeper and begins to flatten out This is known as an inflection point and corresponds to a local maximum on velocity vs. time curve slope stays + just not as steep

positive slope but becoming flatter start out steep slope flattens out as much as it is going to another inflection point corresponds to a relative minimum then slope becomes steeper

positive slope continues to become steeper start out steep

Region 1 – negative slope so negative velocity Region 2 – positive slope so positive velocity but inflection point where slope maxes out Region 3 – positive slope so positive velocity but inflection point where slope is minimized Region 4 – positive slope so positive velocity, no special points so velocity continues to rise

s v a inf max inf