1.2 Kinematics

• Displacement


  The distance of a body from a fixed starting point
• Speed


  How much distance a body covers in a given time
• Velocity


  The rate of change of displacement of a body
• Mean speed


  Distance travelled divided by time taken
• Mean velocity


  Change in displacement divided by time taken
• Instantaneous speed


  The rate at which the distance a body has travelled will change if it remains at this speed
• Instantaneous velocity


  The rate of change of displacement at a time
• Acceleration


  The rate of change of velocity
• Mean acceleration


  Change in velocity divided by time taken
• Instantaneous acceleration


  The rate of change of velocity at a time
• Displacement-time graph


  • Gradient is the velocity of the body
  • Non-straight lines indicate changing velocity and therefore acceleration
• Velocity-time graph


  • Gradient is the acceleration
  • Total area under the graph is the change in displacement
• Speed-time graph


  • Gradient is the magnitude of the acceleration
  • Differs from velocity-time graph when velocity becomes negative
• Deriving the SUVAT equations

  1. Using definitions of velocity, average velocity, and work-energy relationship

  2. Resulting in 4 equations relating displacement, initial velocity, final velocity, acceleration, and time
• Without air resistance, all objects fall at the same rate near the Earth's surface (about 9.8 m/s^2)
• With air resistance, acceleration decreases as speed increases, leading to terminal velocity
• Vertical and horizontal motion

  • Weight acts vertically, so vertical and horizontal motion can be treated separately
  • If there is a uniform velocity in one direction and a uniform acceleration in a perpendicular direction, the two directions can be treated separately