# [SOLVED] Finding the speed from the velocity

• Feb 8th 2009, 08:44 AM
Legendsn3verdie
[SOLVED] Finding the speed from the velocity
ok so the veloctiy is:

v(t) = (-2sint)i + (3cost)j +4k

so to find the speed you do

squareroot((-2sint)^2 + (3cost)^2 +(4k)^2)
=
squareroot(4sin^2t + 9cos^2t + 16k^2)

the book says the speed is 2 * squaroot(5)

i have no idea how to get that from where i left it off.
• Feb 8th 2009, 08:57 AM
skeeter
$\displaystyle v(t) = -2\sin{t} \, \vec{i} + 3\cos{t} \, \vec{j} + 4 \, \vec{k}$

$\displaystyle |v| = \sqrt{4\sin^2{t} + 9\cos^2{t} + 16} = \sqrt{5\cos^2{t} + 20}$

the speed depends on t ... for what time, t = ? , did the problem want you to calculate the speed?
• Feb 8th 2009, 09:05 AM
Legendsn3verdie
Quote:

Originally Posted by skeeter
$\displaystyle v(t) = -2\sin{t} \, \vec{i} + 3\cos{t} \, \vec{j} + 4 \, \vec{k}$

$\displaystyle |v| = \sqrt{4\sin^2{t} + 9\cos^2{t} + 16} = \sqrt{5\cos^2{t} + 20}$

the speed depends on t ... for what time, t = ? , did the problem want you to calculate the speed?

t = pie/2
• Feb 8th 2009, 09:56 AM
skeeter
$\displaystyle |v| = \sqrt{5\cos^2\left(\frac{\pi}{2}\right) + 20} = \sqrt{20} = 2\sqrt{5}$