[SOLVED] Finding the speed from the velocity

**Legendsn3verdie** · Feb 8th 2009, 09:44 AM

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.

**skeeter** · Feb 8th 2009, 09:57 AM

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

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

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

**Legendsn3verdie** · Feb 8th 2009, 10:05 AM

Originally Posted by skeeter

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

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

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

t = pie/2

**skeeter** · Feb 8th 2009, 10:56 AM

$|v| = \sqrt{5\cos^2\left(\frac{\pi}{2}\right) + 20} = \sqrt{20} = 2\sqrt{5}$

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