Position, Velocity, Acceleration vs. Time Plots (1-D)

Questions to ask:

Starting from v vs. t

For velocity graph:

1. Which way is the object moving?
   
• Forward => v > 0
• Backward => v < 0
2. Is it speeding up, slowing down, or moving at constant speed?
   • speeding up => line getting further from 0
   • slowing down => line getting closer to 0
   • constant speed => horizontal line

For acceleration graph:

1. What is the slope of the velocity time graph?
   • Remember that this is piecewise constant in Physics 1 (a simplifying assumption)
     

For the position graph:

1. What is my starting (s₀) value? (Must be given)
2. Which way is the object moving?
   • forward => s should be getting more positive (s values increasing)
   • backward => s should be getting more negative (s values decreasing)
   • no => s is constant (horizontal line)
3. Should the line be curved or straight?
   • Is v constant? => straight
   • Is |v| decreasing? (slowing down) => curved towards horizontal
   • Is |v| increasing? (speeding up) => curved away from horizontal
   • Remember that the s vs. t plot will always produce a smooth curve

Starting from s vs. t

For the velocity graph:

1. What is the slope of the position graph?
   • Remember that our simplifying assumption for the course that all accelerations are constant means that v vs. t will consist of one or more straight lines

For the acceleration graph:

1. What is the slope of the velocity time graph?
   • Remember that this is piecewise constant in Physics 1 (a simplifying assumption)

Starting from a vs. t

For the velocity graph:

1. What is my starting (v₀) value? (Must be given)
2. Given this starting v, is the object speeding up or slowing down?
   • Remember that if v and a have the same direction (sign) then the object is speeding up and if they have opposite direction (sign), then it is slowing down.
   • Remember that acceleration gives the slope of the velocity vs. time graph.
     • A positively sloped line looks like /
     • A negatively sloped line looks like \
   • Remember that our simplifying assumption for the course that all accelerations are constant means that v vs. t will consist of one or more straight lines

For the position graph:

1. What is my starting (s₀) value? (Must be given)
2. Which way is the object moving?
   • forward => s should be getting more positive (s values increasing)
   • backward => s should be getting more negative (s values decreasing)
   • no => s is constant (horizontal line)
3. Should the line be curved or straight?
   • Is v constant? => straight
   • Is |v| decreasing? (slowing down) => curved towards horizontal
   • Is |v| increasing? (speeding up) => curved away from horizontal
   • Remember that the s vs. t plot will always produce a smooth curve