IBMaths: AA HLDPRevision Notes3. Geometry & Trigonometry3.10 Vector Equations of Lines3.10.2 Applications to Kinematics

Applications to Kinematics (DP IB Maths: AA HL)

Revision Note

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Kinematics using Vectors

How are vectors related to kinematics?

  • Vectors are often used in questions in the context of forces, acceleration or velocity
  • If an object is moving in one dimension then its velocity, displacement and time are related using the formula s = vt
    • where s is displacement, v is velocity and t is the time taken
  • If an object is moving in more than one dimension then vectors are needed to represent its velocity and displacement
    • Whilst time is a scalar quantity, displacement and velocity are both vector quantities
  • For an object moving at a constant speed in a straight line its velocity, displacement and time can be related using the vector equation of a line
    • r = a + lambdab
    • Letting
      • r be the position of the object at the time, t
      • a be the position vector, r0 at the start (t = 0)
      • lambda represent the time, t
      • b be the velocity vector, v
    • Then the position of the object at the time, t can be given by
      • r = r0 + t v
    • The speed of the object will be the magnitude of the velocity |v |

Exam Tip

  • Kinematics questions can have a lot of information in, read them carefully and pick out the parts that are essential to the question
  • Look out for where variables used are the same and/or different within vector equations, you will need to use different techniques to find these

Worked example

A car, moving at constant speed, takes 2 minutes to drive in a straight line from point A (-4, 3) to point B (6, -5).

At time t, in minutes, the position vector (p) of the car relative to the origin can be given in the form bold italic p equals bold italic a plus t bold italic b. 

Find the vectors a and b.

3-10-2-ib-aa-hl-kinematics-vectors-we-solution

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Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.