Kinematics

• The area under a velocity vs time graph gives the displacement

  
• The gradient of a velocity vs time graph gives the acceleration

  
• Acceleration


  The rate of change of velocity
• Vectors


  Physical quantities that have both magnitude and direction
• Scalars


  Physical quantities that have magnitude only
• Frame of reference


  A reference point combined with a set of directions
• Rectilinear motion


  Motion along a straight line

  
• Position (x)


  An object's location relative to a reference point

  
• Distance (d)


  The length of path travelled (a scalar quantity)
• Displacement

  A change in position (a vector quantity)

  
• Speed (s)


  The rate of change of distance (a scalar quantity)

  
• Velocity (v)


  The rate of change of position, displacement, or change of displacement (a vector quantity)

  
• Instantaneous velocity


  The velocity of an object measured over a very small time frame
• Average speed


  Total distance / Duration

  
• Average velocity


  Total displacement / Duration
• Distance (d)


  The length of path travelled
• Distance


  • Depends on the path taken
  • Direction ignorant
  • Is a scalar
  • Can never reduce or be negative
• Displacement


  • Independent of path taken
  • Direction aware
  • Is a vector
  • Can reduce and be negative
• Speed (s)


  The rate of change of distance

  
• Velocity (v)


  The rate of change of position OR the rate of displacement OR the rate of change of displacement

  
• Acceleration (a)


  The rate of change of velocity
• Sign of position


  Tells you in which direction you are relative to the reference point

  
• Sign of velocity


  Tells you which way you are going - the reference point is irrelevant

  
• Anytime an object's velocity is changing, the object is said to be accelerating
• If an unbalanced (or net) force acts on an object, the object can change its speed i.e. it is accelerating
• The direction of the acceleration vector is ALWAYS in the same direction as the net force vector
• Deceleration


  Describes an object slowing down
• If an object is slowing down, then its acceleration and the net force acting on it are in the opposite direction of its motion
• vf


  Instantaneous final velocity
• Acceleration


  Measured in meters per second, per second → m.s-2
• Ticker tape diagrams


  • A large distance between the dots indicates that the object was moving fast during that time interval
  • A small distance between dots means the object was moving slowly during that time interval
  • A constant distance between dots represents a constant velocity, and zero acceleration
  • A changing distance between dots indicates a changing velocity and thus an acceleration. The object could be getting faster or getting slower

  
• Acceleration does not provide any information about the velocity or position of an object, but only about how the velocity is changing. It is not possible to tell how fast or in which direction an object is moving from the acceleration alone

  
• The direction of the acceleration is ALWAYS in the same direction as the net force causing the acceleration
• A positive acceleration does NOT necessarily mean the object is increasing velocity, and a negative acceleration does not necessarily mean that the object is slowing down
• Average velocity


  Calculated using the formula: average velocity = displacement / time

  
• Velocity


  The rate of change of position with respect to time

  
• If y is proportional to x, the graph of y vs x is a straight line
• Displacement and time


  Directly proportional for constant velocity motion

  
• Gradient of a position vs time graph


  Represents the velocity of the object

  
• Steeper gradients mean greater velocities