Kinematics (Edexcel IGCSE Maths)

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

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

• 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

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

• Velocity is a function of time, t, and is the rate of change of displacement
  • To find v, differentiate s, ie.
    If s = t³ - 2t²

    then  = 3t² – 4t

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

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

• Acceleration is a function of time, t, and is the rate of change of velocity
  • To find a, differentiate v, ie. 
    If v = 3t² – 4t

    then = 6t - 4

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

How do I solve kinematics problems?

• Be clear about how the three quantities are related through differentiation
  • 
  • 

• 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)