Kinematics (Edexcel IGCSE Maths)

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Mark

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Mark

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What does kinematics mean?

  • Kinematics is the study of the motion of a particle (object) linking the three vector quantities displacement, velocity and acceleration
  • Motion is in a straight line – think of the particle as moving along a number line
    • The number line has a fixed point O (the origin)
    • The number line has both negative and positive values
    • The particle can move in both directions along the number line

  • Note that in kinematics, a particle is an object – it could be a football, a car, a train - anything that has motion.  A particle is modelled as taking up a single point in space

 Kin Notes fig1, downloadable IGCSE & GCSE Maths revision notes

What is displacement and how is it different to distance?

  • Displacement measures how far the particle is from the origin and is a vector quantity, so it can be negative
    • Distance is always positive

  • Displacement is measured from the fixed point O
  • The letter s is used for displacement
    • It is usually measured in metres (m)

  • If s = 4 then the distance from the origin is 4 m and the particle is 4 m “in front of” the origin
  • If s =-5 then the distance from the origin is 5 m and the particle is 5 m “behind” the origin
  • The + or - indicates the particle’s position relative to the origin

 

Kin Notes fig2, downloadable IGCSE & GCSE Maths revision notes

  • Displacement is a function of time, t, where time is usually measured in seconds
    • eg. s = 3t3 - 2t + 1

      At time t = 0, s = 1

      At time t = 2, s = 21

 

Kin Notes fig3, downloadable IGCSE & GCSE Maths revision notes

What is velocity and how is it different to speed?

  • Velocity measures how fast the particle is travelling and is a vector quantity, so it can be negative
    • Speed is always positive

  • The letter v is used for velocity
    • It is usually measured in metres per second (m/s)

  • If v = 3 then the speed of the particle is 3 m/s and it is moving in the positive direction
  • If v = -6 then the speed of the particle is 6 m/s and it is moving in the negative direction
  • The + or - indicates the particle’s direction of motion

 Kin Notes fig4, downloadable IGCSE & GCSE Maths revision notes

  • Velocity is a function of time, t, and is the rate of change of displacement
    • To find v, differentiate s, ie. bold italic v bold equals fraction numerator bold d bold s over denominator bold d bold t end fraction

      If s = t3 - 2t2

      then bold italic v bold equals bold ds over bold dt = 3t2 – 4t

  • If velocity is zero then the particle is stationary (not moving)

 Kin Notes fig5, downloadable IGCSE & GCSE Maths revision notes

What is acceleration?

  • Acceleration measures how fast the velocity is change and is a vector quantity, so it can be negative
    • The magnitude of acceleration is always positive

  • The letter a is used for acceleration
    • It is usually measured in metres per square second (m/s2)

  • If a = 1 then the magnitude of acceleration is 1 m/s2 and the particle is accelerating (velocity increasing / speeding up)
  • If a = -6 then the magnitude of acceleration is 6 m/s2 and the particle is decelerating (velocity decreasing / slowing down)
  • The + or - indicates whether the particle is accelerating or decelerating

 Kin Notes fig6, downloadable IGCSE & GCSE Maths revision notes

  • Acceleration is a function of time, t, and is the rate of change of velocity
    • To find a, differentiate v, ie. bold italic a bold equals fraction numerator bold d bold v over denominator bold d bold t end fraction

      If v = 3t2 – 4t

      then bold italic a bold equals bold dv over bold dt= 6t - 4

  • If acceleration is zero then the particle is moving at a constant velocity

 Kin Notes fig7, downloadable IGCSE & GCSE Maths revision notes

How do I solve kinematics problems?

  • Be clear about how the three quantities are related through differentiation
    • bold italic v bold equals bold ds over bold dt
    • bold italic a bold equals bold dv over bold dt

 

Kin Notes fig8, downloadable IGCSE & GCSE Maths revision notes

  • There are some key phrases to look out for
    • Initial / initially means when t = 0 (at the start)
    • At rest means when v = 0 (not moving, no velocity)
      • If the rest is only at one point in time (in an instant) then it is instantaneous rest
      • For example, find the value of t for which the particle is at instantaneous rest (solve v = 0 to find t)

Kin Notes fig9, downloadable IGCSE & GCSE Maths revision notes

Examiner Tip

Displacement, velocity and acceleration can all be negative whereas distance, speed and magnitude of acceleration are always positive.

Worked example

Kin Example fig1 sol, downloadable IGCSE & GCSE Maths revision notes

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Mark

Author: Mark

Expertise: Maths

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.