I have a project where we have to throw an object and find the velocity of it. I have found the parametric equations of the path of the object to be:
$$x(t)=0.627273t+(−0.211364)$$ $$y(t)=−0.658275t^2+1.96578t+0.014545$$
I have found that the initial velocity vector is:
$$v^2 = 0.627273^2 + 1.96578^2$$ $$v = 2.06343461853$$ $$v(t) = (0.627273,1.96578)$$ Firstly, is this correct?
Secondly, we are required to make a diagram showing the initial velocity vector and the components. How am I to do this accurately on the graph (in Desmos)?
Your initial velocity vector is correct but your $v(t)$ is incorrect. It should be:
$$v(t)=(0.627273, -1.31655t+ 1.96578)$$
Yes, the velocity in the $y$ direction changes over time. At the initial time, $t=0$ and that first term in the $y$ component disappears. A true $v(t)$ is then found from these components:
$$v(t)= \sqrt{0.627273^2 + (-1.31655t+ 1.96578)^2}$$