Question

(1 point) Suppose the position of a particle in motion at time t is given by the vector parametric equation r(t) = (3/t - 2), 7, 2+3 – 6t). (a) Find the velocity of the particle at time t. v(t) = (b) Find the speed of the particle at time t. Speed = (c) Find the time(s) when the particle is stationary. If there is more than one correct answer, enter your answers as a comma separated list. t =

Answer 1

Solution the position of the partice in motion at time 4* is given by : * Plt)= < 36t-2)2, 4, 443-672) (a) How , the velocity of the particle at time t. velocity ult) = rilt vlt) = ( 6(7-2), 0, 67=12t>| (b) speed of the particle at time't is speedo lvet) la magnitude of its speed = 176(-2)32+ 02+(6+2+12+)2 speed = 146 14 -2)}2 + 46+Ct -2)}? speed = 546(-2)}2 (1+ t?) speeds: 6(t-2) JU+ t2j unit (©) when the particle is in stationary thin (speed) : velocity is zero, then 6 (t-2) JHt? ao t=2 ttl t=2, +?=-1,which is not possible. Hence, [t= 2 unit