# Thread: magnitude of velicity vector

1. ## magnitude of velicity vector

I have a velocity vector:

6 t cos(t^2) i - 6 t sin (t^2) j and I need to get the magnitude of this. I put it under the square root sign while squaring both terms and adding them together. The answer is 6 l t l but I can not figure out why!!!! Anyone able to explain would be very much appreciated. Frostking

2. Originally Posted by Frostking
I have a velocity vector:

6 t cos(t^2) i - 6 t sin (t^2) j and I need to get the magnitude of this. I put it under the square root sign while squaring both terms and adding them together. The answer is 6 l t l but I can not figure out why!!!! Anyone able to explain would be very much appreciated. Frostking
So you got
$\displaystyle \sqrt{36 t^2 cos^2(t^2)+ 36 t^2 sin^2(t^2)}$
$\displaystyle = \sqrt{36 t^2 (cos^2(t^2+ sin^2(t^2))}$
What is $\displaystyle sin^2(t^2)+ cos^2(t^2)$?

What is $\displaystyle \sqrt{36}$

What is $\displaystyle \sqrt{t^2}$?

Be careful with that last one! Think about t= -2.