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 slopebut 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 pointand 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 asit is going to another inflection point

corresponds to a relative minimumthen 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