I've run into a road block studying for Math 125. So here is a math question for all you geniuses...

How do I get the instantianious speed at a certain time t when I am given two parametric equations, x(t) and y(t) which are the position functions of the particle at time t? I tried finding the derivative, which would give me speed/velocity, so I would have x'(t) and y'(t), then I would plug in t, unfortunately pluging in t for both functions resulted in a different value for each. How do I go about doing this problem?

The second part is finding the average speed over a period of time. I was thinking distance over time. Since the parametric equation for position is a curve, I plugged it into the arc length function. Since I figure average speed is distance over time. So I'm thinking I put arc length over the entire period of time. Is this right? Am I missing anything? Any mistakes?

post the question and maybe i can do it

position functions...

x(t) = 3t
y(t) = 4/3 t^(3/2), 0<t<4

so you get...

x'(t) = 3dt
y'(t) = 2 t^(1/2)

looking for speed at time t = 4...

...second part...

...average speed of the particle over the time interval 0<t<4...

:O

Yeah, instantaneous speed is what you said
vx(4)=3
vy(4)=4
If you want the module simply do the square root af adding the squares of the velocities in each axis, so v=5

In the average of the speed it does not matter how is speed increased, just take the space runned and divide it by time
vx=3
vy= 4/3 4^(3/2) / 4
if you want the module calcule it in the same way

Palloco beat me too it :( i was at work
he is right ;)

yeah um... I was doing it too... yeah