# maximum velocity of a particle with 3d vector equation

• February 6th 2010, 06:14 PM
shawli
maximum velocity of a particle with 3d vector equation
Find the maximum speed of a particle whose velocity v m/s, at any time t seconds is given by v $=2sin(t)$ i $+ cos(t)$ j $+ 3$ k.
• February 7th 2010, 12:36 AM
Sudharaka
Quote:

Originally Posted by shawli
Find the maximum speed of a particle whose velocity v m/s, at any time t seconds is given by v $=2sin(t)$ i $+ cos(t)$ j $+ 3$ k.

Dear shawli,

$v=2\sin{t}\underline{i}+\cos{t}\underline{j}+3\und erline{k}$

$Therefore,~speed~of~the~particle~(S)=\left|2\sin{t }\underline{i}+\cos{t}\underline{j}+3\underline{k} \right|$

$S=\sqrt{(2sint)^2+cos^{2}t+9}$

$S=\sqrt{3sin^{2}t+10}$

$Since,~(sin^{2}t)_{max}=1$

$S_{max}=\sqrt{13}\approx{3.61}$

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