Variable Acceleration

• Particle P


  Moving on the x-axis
• Displacement x


  Metres from O at time t seconds, given by x = t^4 - 32t + 12
• Find:


  1. Velocity of P when t = 3

  2. Value of t for which P is instantaneously at rest

  3. Acceleration of P when t = 1.5
• You can use calculus to determine maximum and minimum values of displacement, velocity and acceleration
• Yo-yo distance s


  s = 0.6t + 0.4t^2 - 0.2t^3, 0 <= t <= 3
• Find:


  Maximum distance of the yo-yo from the child's hand
• Displacement x


  x = ∫v dt = 3t^2 - t^3/3 + 5
• You can use calculus to derive the formulae for motion with constant acceleration
• Displacement s


  s = 2t^3 - 3t
• Velocity v


  v = ds/dt
• Acceleration a


  a = dv/dt = d^2s/dt^2
• • Increasing acceleration: gradient of velocity-time curve increases
  • Decreasing acceleration: gradient of velocity-time curve decreases