Analysis of a Distance vs. Time Graph

Determining the motion on a D vs. T Graph Where did the object start? Which direction did it go? Where did the object stop? Is the motion uniform (constant)? Is the motion non-uniform (changing)? Can you tell which is faster? (if 2 or more objects are present)

Object A is stationary at some positive position from the origin. d(m) A Object A is stationary at some positive position from the origin. t(s)

Object B moves away from origin with a constant positive velocity. d(m) B Object B moves away from origin with a constant positive velocity. t(s)

d(m) C Object C start at some positive position and moves away from the origin at a constant positive velocity. t(s)

d(m) Object D moves away from the origin at a constant positive velocity (slower than previous examples). D t(s)

d(m) Object E start at some positive position and walks toward the origin with a constant velocity. E t(s)

Distance vs. Time Graphs with Non-Uniform Motion Changing velocity (increasing) Changing velocity (decreasing)

Average Velocity (Vav) Slope of a D vs. T Graph Rise/run On a distance vs. time graph Rise = df – di = Δd Run = tf – ti = Δt Slope = Δd / Δt =… Average Velocity (Vav)

Using slope to predict motion On a distance vs. time graph If slope is 0, then velocity is 0. If slope is positive, velocity is constant in positive direction. If slope is negative, velocity is constant in the opposite direction. If slope is changing, velocity is changing.(i.e. you are accelerating)

Same velocity as B. Constant +V V=0 Slower than B or C. d(m) C B A D t(s)

E A East B High St. D C West

Vavg = Δd / Δt Vavg = (df –di)/Δt df = di + Vavg Δt Finding position Vavg = Δd / Δt Vavg = (df –di)/Δt df = di + Vavg Δt (df = final position)