bicen maths

• When analysing a velocity-time graph, the gradient represents the acceleration
• Acceleration can be variable, meaning it is constantly changing
• In a velocity-time graph, if the acceleration is increasing, the graph will become steeper
• Initial velocity


  The velocity at time t=0
• Instantaneously at rest


  The body is at rest for a brief moment, but may not remain at rest
• Finding the value of t when velocity is 64 m/s


  1. Set the velocity equation equal to 64

  2. Solve the quadratic equation
• The greatest speed of the body occurs between t=0 and t=5 seconds
• Velocity-time graph


  • The maximum speed corresponds to the highest point on the graph in the given time interval
• The maximum speed is 24 m/s
• A particle P is moving on the x axis at time T seconds
• Displacement X


  Meters from O, given by the function T^4 - 32T + 14
• Finding velocity


  Differentiate displacement with respect to time to get velocity
• Velocity V = 4T^3 - 32
• When particle P is at rest

  Velocity V = 0
• Finding time when particle P is at rest

  Set velocity V = 0 and solve for T
• Acceleration A = 12T^2
• Finding acceleration


  Differentiate velocity with respect to time to get acceleration
• Cat's displacement from house in meters is T^3 - 3/2T^2 - 36T
• Finding velocity of cat

  Differentiate displacement with respect to time to get velocity
• Cat's velocity when T = 2 is -30 m/s
• When cat is instantaneously at rest

  Velocity V = 0
• Finding time when cat is at rest

  Set velocity V = 0 and solve for T
• Cat's acceleration after 5 seconds is 27 m/s^2
• Relationship between displacement, velocity and acceleration


  • Displacement is differentiated to get velocity, velocity is differentiated to get acceleration