Question

A particle vector is given by r=2ti+t^2j. Find: (a) r at t=1 and t=3, respectively;
(b) the displacement of particle from t=1 to t= 3.
(c) the path equation of the particle

Answer 1

$\vec r=\vec r(t)=2t\vec i+t^2 \vec j=(2t,t^2)$

(a) $\vec r(1)=(2,1),\,\, \vec r(3)=(6,9)$

(b) $\Delta \vec r=\vec r(3)-\vec r(1)=(4,8)$

(c) $x=2t,\, y=t^2 \rightsquigarrow y=0.25x^2$ is the path equation