I'm trying the next problem:
A particle is moving along parabola y=x^2 at constant speed k, find r(t), v(t), a(t), according book we can simply substitute x=t, and y=t^2,
So r(t)=[t,t^2], v(t)=[1,2t], a(t)=[0,2] but if particle is moving at constant speed then||v(t)||= k and what we really have is v(t)=[1,2t] -> ||v(t)||=sqrt(1+4 t^2).
At this point I don't know how to proceed in order to get r(t), v(t), a(t), any hint please.
A particle is moving along parabola y=x^2 at constant speed k, find r(t), v(t), a(t), according book we can simply substitute x=t, and y=t^2,
So r(t)=[t,t^2], v(t)=[1,2t], a(t)=[0,2] but if particle is moving at constant speed then||v(t)||= k and what we really have is v(t)=[1,2t] -> ||v(t)||=sqrt(1+4 t^2).
At this point I don't know how to proceed in order to get r(t), v(t), a(t), any hint please.