Kinematics Toolkit (Edexcel IGCSE Further Maths)

What is kinematics?

• Kinematics is the branch of mathematics that models and analyses the motion of objects
• Common words such as distance, speed and acceleration are used in kinematics
  • But are used according to their technical definition

What terminology do I need to be aware of?

• Firstly, only motion of an object in a straight line is considered
  • This may be described as motion 'along the -axis'
  • The straight line will have a positive and a negative direction
    • On the -axis this will be the usual positive and negative directions
    • If the question doesn't specify, you can choose the positive and negative directions
    • (Just be consistent once you've made a choice!)
• Particle
  • A particle is the general term used for an object
  • A particle is assumed to be the 'size' of a single point
    • So you don't need to worry about its 3D dimensions!
• Time  
  • Time is usually measured in seconds ()
  • Displacement, velocity and acceleration are all functions of time
  • 'Initial' or 'Initially' means 'when '
• Displacement 
  • is the usual notation for displacement
    • Don't confuse that with the  for seconds!
    • For motion along the -axis,  may be used instead of 
  • Displacement is usually measured in metres ()
  • The displacement of a particle is its distance relative to a fixed point
    • The fixed point may be (but is not always) the particle’s initial position
    • For motion on the -axis the fixed point will be the origin
    • Read the question carefully, and don't assume!
  • Displacement will be zero, , when the object is at the fixed point
  • Otherwise the displacement will be
    • positive if the particle is in the positive direction from the fixed point
    • or negative if it is in the negative direction from the fixed point

• Distance
  • Distance is also usually measured in metres ()
  • Use of the word distance could refer to
    • the distance travelled by a particle
    • the (straight line) distance the particle is from a particular point
  • Be careful not to confuse displacement with distance
    • e.g. for a bus starting and ending its journey at a bus depot,
    • its displacement will be zero when it returns to the depot
    • but the distance the bus has travelled will be the length of the route
  • Distance is always positive
• Velocity 
  • Velocity is usually measured in metres per second (  or  )
  • The velocity of a particle is the rate of change of its displacement at time
    • Velocity will be positive if the particle is moving in the positive direction
    • Or negative if it is moving in the negative direction
  • If the particle is stationary, that means the velocity is zero, 
    • '(Instantaneously) at rest' also means that 
• Speed
  • Speed is also usually measured in metres per second (  or  )
  • Speed is the magnitude (i.e. absolute value or modulus) of the velocity
    • i.e. speed 
  • For a particle moving in a straight line
    • speed is the 'velocity ignoring the direction'
    • if,  speed 
    • if ,  speed = 
• Acceleration
  • Acceleration is usually measured in metres per second squared (  or  )
    • That is the same as metres per second per second
  • The acceleration of a particle is the rate of change of its velocity at time
  • Acceleration can be positive or negative
    • but the sign alone cannot fully describe the particle’s motion
  • If velocity and acceleration have the same sign
    • then the particle is accelerating (speeding up)
  • if velocity and acceleration have different signs
    • then the particle is decelerating (slowing down)
  • At times when the acceleration is zero, ,
    • the particle is moving with constant velocity 
  • In all cases the direction of motion is determined by the sign (+ or -) of the velocity