Calculus Vector Curves

Question

A point has a position vector given by  , for all time t ≥ 0 seconds. Find the speed of the object at t = 3 seconds. (4 points)

I chose this	1
	0

I took the derivative of r(t) to get the velocity vector, which is (1,0), sqrt(1^2+0)=1. I don't know if I am doing this correctly, please help me, thank you in advance!

Answer 1

Yes, this is perfect. As you've noted, the velocity v(t) is a vector, obtained by taking component-wise derivatives (with respect to the parameter t) of the position vector r(t). The speed, being the magnitude of the velocity vector v(t), is the sq-root of the sum of the squares of the components of v(t).