Question

someone fires a pistol and it's bullet leaves the muzzle at t=0. The position vector of the bullet is r= ax+bty ( a and b are postive constants)

what are the units of a and b so the equation to make sense

what's the acceleration and velocity

Answer 1

r is distance (m), so assuming that x and y are also distance,

a(m) = m, so a is just a constant
b(s)(m) = m, so b = 1/s

velocity = r' = ax' + by + bty'
acceleration = r" = ax" + by' + by' + bty"
= ax" + 2by' + bty"

where ' means d/dt