PLEASE HELP
1 answer:
You might be interested in
Answer:
, for all
Step-by-step explanation:
The velocity vector is found by deriving the position vector depending on the time:
In turn, acceleration vector is found by deriving the velocity vector depending on time:
Velocity and acceleration vectors at are:
Norms of both vectors are, respectively:
The angle between both vectors is determined by using the following characteristic of a Dot Product:
Given that cosine has a periodicity of . There is a family of solutions with the form:
, for all
or
is very easy to graph.
Choose whatever value of and use the same for
in the same coordinate. Repeat and strike a line through all the points.
Some examples of valid points would be: ,
,
and
.
Then, to graph you have to look at it in terms of the equation of a line (
) and its parts.
In this case, and
.
So, you choose any value for and you solve to find its
counterpart.
I will start with :
Now, we have a first coordinate: .
Repeat with a different value:
It gives us the coordinates .
Plot those into the graph and strike a line through them.
Wherever the two lines in your Cartesian Plane cross, that is the solution for both equations. It should be .
You can check it by replacing and
by "3" in both formulas and equating the values of
:
Your solution is worked out and checked to be correct.
PS: I am attaching a picture of the graph, so you can have a visual idea of what it should look like.
