Applications to Kinematics (DP IB Maths: AA HL)

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 |