Menu Close

Solve-A-particle-moves-along-the-space-curve-r-t-2-t-i-3t-2-j-2t-3-4t-2-k-find-a-velocity-b-speed-or-magnitude-of-velocity-c-acceleration-d-magnitude-of-acceleration-at-time-t-2-




Question Number 200736 by Calculusboy last updated on 22/Nov/23
Solve: A particle moves along the space  curve r_− =(t^2 +t)i+(3t−2)j+(2t^3 −4t^2 )k.  find  (a)velocity  (b)speed or magnitude of velocity  (c)acceleration  (d)magnitude of acceleration at time t=2
$$\boldsymbol{{Solve}}:\:\boldsymbol{{A}}\:\boldsymbol{{particle}}\:\boldsymbol{{moves}}\:\boldsymbol{{along}}\:\boldsymbol{{the}}\:\boldsymbol{{space}} \\ $$$$\boldsymbol{{curve}}\:\underset{−} {\boldsymbol{{r}}}=\left(\boldsymbol{{t}}^{\mathrm{2}} +\boldsymbol{{t}}\right)\boldsymbol{{i}}+\left(\mathrm{3}\boldsymbol{{t}}−\mathrm{2}\right)\boldsymbol{{j}}+\left(\mathrm{2}\boldsymbol{{t}}^{\mathrm{3}} −\mathrm{4}\boldsymbol{{t}}^{\mathrm{2}} \right)\boldsymbol{{k}}. \\ $$$$\boldsymbol{{find}} \\ $$$$\left(\boldsymbol{{a}}\right)\boldsymbol{{velocity}} \\ $$$$\left(\boldsymbol{{b}}\right)\boldsymbol{{speed}}\:\boldsymbol{{or}}\:\boldsymbol{{magnitude}}\:\boldsymbol{{of}}\:\boldsymbol{{velocity}} \\ $$$$\left(\boldsymbol{{c}}\right)\boldsymbol{{acceleration}} \\ $$$$\left(\boldsymbol{{d}}\right)\boldsymbol{{magnitude}}\:\boldsymbol{{of}}\:\boldsymbol{{acceleration}}\:\boldsymbol{{at}}\:\boldsymbol{{time}}\:\boldsymbol{{t}}=\mathrm{2} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *