L7 - Linear Kinematic Quantities

• Position (s):

  • Need a reference frame (to find position)
  • Scalar
  • Symbol for position = s
• Distance & Displacement:

  • Both are descriptions of change in position
• Distance:

  • Change in position
  • Scalar (d)
  • The magnitude
  • Distance travelled → No info in direction of movement
  • Length of path
  • From start to end point, stretch out whole difference
• Displacement:

  • Change in position
  • Vector (d)
  • Magnitude & direction
  • Difference bw/ initial & final position
  • Straight line, furthest apart
  • Centre to goal
  • d = Δs = sf - si
  • = (final - initial)
  • Tells direction
• Rate of Change:

  • Slope of a graph gives the rate of change in y with respect to x (normally time)
  • Slope = rise/run = Δ y/Δ x
  • eg tells us how quickly changing position/velocity/acceleration (y) etc, in relation to time (x)
• Speed & Velocity:

  • Speed
  • Rate of change of distance
  • v = d/Δ t
  • Velocity
  • Rate of change in position/displacement (know direction)
  • v = d/Δ t
  • Increase top number (d), increases v
  • Increasing bottom number (Δ t), decreases v
• Derivative Graphs:

  • +ve slope → +ve velocity
  • Constant slope → constant velocity
  • Increasing slope → increasing velocity
• Derivative Graphs:

  • 1st time chunk, any change in x (time) results in a change in position
  • Rate of change is constant (speed not changing)
  • If steep increase speed higher
  • No slope = position not changing
  • Becomes less steep, at the peak/apex slope = 0 velocity
  • Curvature: pos = hill, neg = valley
  • Velocity: curvature constantly increasing for a constant increase in speed (1st chunk)
• Acceleration:

  • Speeding up/slowing down
  • Rate of change of speed
  • Not interested in direction
  • a = Δ v/Δ t
  • Acceleration
  • Rate of change of velocity
  • a = Δ v/Δ t
• Derivative graphs:

  • +ve velocity slope → +ve acceleration
  • Constant velocity slope → constant accelerating
  • Increasing velocity slope → increasing acceleration
• Derivative Graphs:

  • Constant acceleration, pos = slope, pos acceleration & vise versa
  • Curvature: pos = hill, neg = valley
• Acceleration Direction:

  • Also have to think about direction of acceleration
  • Reference frame needed
  • Pos & neg = neg
  • Neg & neg = pos