What is kinematics?

• Kinematics?is the analysis of the motion of a?particle?linking the three vector quantities?displacement,?velocity?and?acceleration?– see below
• 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

• Ensure you are familiar with Differentiation - Basics andDifferentiation – Turning Points before continuing
• It may be wise to look at Differentiation – Problem Solving too

What is displacement; isn’t it the same as distance?

• Displacement?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 = 1At time?t = 2,?s = 21

   

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What is velocity; isn’t it the same as speed?

• Velocity?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 5 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.?v = ds/dt 

    If?s = t³?- 2t²then?v = ds/dt = 3t²?– 4t

   

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

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What is acceleration?

• Acceleration?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)
• If?a = -6?then the magnitude of acceleration is 6 m/s²?and the particle is?decelerating?(velocity decreasing)
• The + or - indicates whether the particle is?accelerating?or?decelerating

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• Acceleration?is a function of?time,?t, and is the?rate of change?of?velocity
  • To find?a, differentiate?v, ie.?a = dv/dt 

    If?v = 3t²?– 4tthen?a = dv/dt = 6t - 4

   

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

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How do I solve kinematics problems?

• Be clear about how the three quantities are related through differentiation
  • v = ds/dt
  • a = dv/dt

   

• There are some key phrases to look out for
  • “...?initial?...” / “...?initially?...” 

    This means at the?start, so when?t = 0

  • “... at?rest?...” 

    This means the particle is?stationaryso?v = 0

  • “...?instantaneously?...”This means at some point in time, for some value of t

   

• For example,“Find the value(s)s of?t?for which the particle is instantaneously at rest”
  • means find the time(s) when?v = 0,
  • ie. solve the equation?v = 0