16. application of vectors

16.1 describing motion in two dimensions

  • (2D) vectors: displacement, velocity, acceleration

  • (2D) scalars: distance, speed

  • av velocity = displacement/time , av speed = distance/time

  • displacement is the difference between the position vectors

  • distance is the square root of the displacement

  • av speed is not the square root of displacement WHEN there’s a change in direction.

  • trajectory is the path of an object.

  • if a particle starts at the point with position vector r0 and moves with a constant velocity v, its position vector at time t i s r = r0 + vt

  • two particles meet if RA = RB for the same value of t

16.2 constant acceleration equations

  • SUVAT

16.3 calculus with vectors

  • integration and differentiation is done independently,

  • s → v → a

  • t = 0 so v = 0 (c = 0)

16.4 vectors in three dimensions

  • magnitude of a vector is their sum square rooted,

  • the distance between position vectors, |first - second|.

16.5 solving geometrical problems

  • midpoint of AB is ½ (a+b)

  • a and b are parallel? b = k a

  • unit vector is a / |a|