Graphs of motion

• Distance-Time Graphs

  • A distance-time graph shows how the distance of an object moving in a straight line (from a starting position) varies over time

  A) increasing

  
• Constant Speed on a Distance-Time Graph

  • Distance-time graphs also show the following information:
  • If the object is moving at a constant speed
  • How large or small the speed is
  • A straight line represents constant speed
  • The slope of the straight line represents the magnitude of the speed:
  • A very steep slope means the object is moving at a large speed
  • A shallow slope means the object is moving at a small speed
  • A flat, horizontal line means the object is stationary (not moving)
• Changing Speed on a Distance-Time Graph

  • Objects sometimes move at a changing speed
  • This is represented by a curve
  • In this case, the slope of the line will be changing
  • If the slope is increasing, the speed is increasing (accelerating)
  • If the slope is decreasing, the speed is decreasing (decelerating)
• CONSTANT SPEED:

  A) larger

  B) smaller

  
• CHANGING SPEED:

  A) decreasing

  B) increasing

  
• Gradient of a Distance-Time Graph

  • The speed of a moving object can be calculated from the gradient of the line on a distance-time graph:

  
• Area Under Velocity-Time Graphs

  • The area under a velocity-time graph represents the displacement (or distance travelled) by an object
• • If the area beneath the graph forms a triangle (i.e. the object is accelerating or decelerating), then the area can be determined by using the following formula:

  Area = ½ × Base × Height

  • If the area beneath the graph forms a rectangle (i.e. the object is moving at a constant velocity), then the area can be determined by using the following formula:

  Area = Base × Height
• Determining Distance from a Velocity-Time Graph

  • Enclosed areas under velocity-time graphs represent total displacement (or total distance travelled)
  • If an object moves with constant acceleration, its velocity-time graph will comprise of straight lines
  • In this case, calculate the distance travelled by working out the area of enclosed rectangles and triangles as in the image above