Analyzing Graphs Quiz

Distance

Total length of the path taken

Speed

The distance traveled per unit of time (uses distance)

Position

The location of an object at a time

Displacement

The difference in starting and ending position

Velocity

The change in position per unit of time (uses displacement)

Acceleration

The change in velocity per unit of time

Vector

A quantity that has both magnitude and direction

Scalar

A quantity that only has magnitude

Rules for analyzing motion of Position vs. Time Graphs:

• Sign on the slope determines the direction (+ = right, - = left)

• Straight horizontal lines mean object is at rest

• Slope of a p vs. t graph is the velocity

Rules for analyzing motion of Velocity vs. Time graphs:

• Lines being above or below the x-axis determines the direction (Ex. x > 0 → right x < 0 → left)

• Straight horizontal line means the object is moving at a constant velocity

• ± slope determines if object is slowing down or speeding up

• Slope of a V vs. T graph yields acceleration

Velocity increasing/decreasing rules based on V vs. T graph

• If v+ & a+ = velocity increase

• If v+ & a- = velocity decrease

• If v- & a+ = velocity decrease

• If v- & a- = velocity increase

• If acceleration is in the same directions as velocity THEN velocity will be increasing

Analysis using AUC (Area under the curve) V vs. T graph

• AUC yields displacement for V vs. T graph

  1. Break up each interval into either a triangle or a rectangle

  2. For each shape, determine the base and height

  3. Use area equations for rectangles & triangles

  4. Use proper units (AND SIGNAGE DEPENDING ON WHAT YOU’RE SOLVING FOR)

V vs. T graph to A vs. T graph conversion

1. Calculate slopes for each interval of V vs. T graph

2. Mark each interval on the time axis

3. Scale the acceleration axis to fit all accelerations

4. Draw the acceleration lines for each interval one at a time

   • Constant acceleration = flat line

V vs. T graph to P vs. T graph conversion

1. Calculate the AUC for each interval

2. Mark e