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 + λb
- 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 + tv
- The speed of the object will be the magnitude of the velocity |v |
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 .
Find the vectors a and b.