Applications to Kinematics (DP IB Analysis & Approaches (AA)): Revision Note

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 + b

  • Letting

    • r be the position of the object at the time, t

    • a be the position vector, r₀ at the start (t = 0)

    •  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 |