Kinematics Toolkit (Edexcel IGCSE Further Pure Maths)

Displacement, Velocity & Acceleration

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