Instantaneous Velocity

Sully

Hi folks,
Can someone tell me what the correct method for Instantaneous Velocity is?

Example;

s= 3t^3 + 2t (where t is in seconds)

- When will its Instantaneous Velocity be 30mts per second?

I was thinking at first get the derivative of the function, then plug the number 30 where t appears, but wasn't sure if I was getting mixed up.

Thanks

LeixlipRed

You want to find the first derivative of s. ds/dt will be your velocity. Then you're asked at what time t will the velocity be 30m/s, so set ds/dt=30 and solve for t.

Sully

So would I be right in saying thats;

s' = 9t^2 + 2
s(30)= 9(30)^2+2

Correct?!

LeixlipRed

No, you're finding the velocity when t=30. Read the question and my reply again.

Sully

Silly me. This is different to velocity I assume, where my original answer would apply?

9t^2 + 2 = 30

Long division?

LeixlipRed

Long division? Not sure what you mean. You need to solve for t in that equation. Any ideas?

Sully

LeixlipRed wrote: »

Long division? Not sure what you mean. You need to solve for t in that equation. Any ideas?

Find a suitable number that when replacing t gives you 30 as the answer. So I need to find the roots?

LeixlipRed

Well I'd suggest isolating t and solving that way as opposed to factorising the quadratic. Though that would work too.

[latex]9t^{2} + 2=30[/latex]
[latex]t^2=\frac{28}{9}[/latex]
[latex]t=\sqrt{\frac{28}{9}}[/latex]

Sully

Thanks for that, appreciated