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
• This graph shows a moving object moving further away from its origin:

  
• 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
• Constant Speed on a Distance-Time Graph:

  • 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)
• This graph shows how the slope of a line is used to interpret the speed of moving objects. Both of these objects are moving with a constant speed, because the lines are straight:

  
• 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)
• Changing speeds are represented by changing slopes. The red line represents an object slowing down and the green line represents an object speeding up:

  
• The speed of an object can be found by calculating the gradient of a distance-time graph:

  
• Velocity-Time Graphs:

  • A velocity-time graph shows how the velocity of a moving object varies with time
  • The red line represents an object with increasing velocity
  • The green line represents an object with decreasing velocity
• Increasing and decreasing velocity represented on a velocity-time graph:

  
• Acceleration on a Velocity-Time Graph:

  • Velocity-time graphs also show the following information:
  • If the object is moving with a constant acceleration/deceleration
  • The magnitude of the acceleration/deceleration
• Acceleration on a Velocity-Time Graph:

  • A straight line represents constant acceleration
  • The slope of the line represents the magnitude of acceleration
  • A steep slope means large acceleration (or deceleration) - i.e. the object's speed changes very quickly
  • A gentle slope means small acceleration (or deceleration) - i.e. the object's speed changes very gradually
  • A flat line means the acceleration is zero - i.e. the object is moving with a constant velocity
• Interpreting the slope of a velocity-time graph:

  
• • The acceleration of an object can be calculated from the gradient of a velocity-time graph:

  
• The gradient of a velocity-time graph: