Hi
We cannot explain something either you haven;t study yet or you forgot it...
Please have a look first here
http://www.ittc.ku.edu/~jstiles/220/...n%20Vector.pdf
Position (vector) - Wikipedia, the free encyclopedia
Can someone explain how to do this question?
"A particle moves such that its position at time t is given by r=(t,t^{2},t^{3}).
Find the rate of change of the distance of the particle from the origin."
I don't understand the way r is described, does it mean the x,y and z coordinates of r? If so, how do you use the chain rule to differentiate this?
Thanks
Laura
Hi
We cannot explain something either you haven;t study yet or you forgot it...
Please have a look first here
http://www.ittc.ku.edu/~jstiles/220/...n%20Vector.pdf
Position (vector) - Wikipedia, the free encyclopedia
First there is just the one independent variable, t, so this is NOT "partial differentiation", just ordinary differentiation.
This is a vector equation: . Do you know how to differentiate t with respect t? What about or .
I am still obviously not fully understanding this and need more of an explanation.
What I have understood so far is that r is a vector with coordinates (x(t),y(t),z(t)). Where x(t)=t, y(t)=t^{2} and z(t)=t^{3}.
In order to find the rate of change of r I must find the derivatives x'(t), y'(t) and z'(t) which are 1, 2t and 3t^{2}, respectively. I also know you can write the coordinates in terms of unit vectors: r= t(i)+t^{2}(j)+t^{3}(k). Is this all correct? What happens to the unit vectors if that is the case?