## anonymous one year ago Find the instantaneous velocity and speed at time 5 secs when v(t) = t2 – 9t + 18 and s(0) = 1

1. anonymous

i figured i would just ave to find the acceleration (which is just the derivative of v(t)) and then plug five into that but i did that and got it wrong

2. Astrophysics

Why would you find acceleration when it's asking for velocity, just plug in 5 for your velocity.

3. anonymous

its asking for the instantaneous velocity doesn't that mean the tangent?

4. Astrophysics

Are you sure it's not suppose to be s(t)

5. anonymous

no i am given v(t)

6. anonymous

but i am also given s(0) so i can just find s(t)

7. Astrophysics

You're given the instantaneous velocity

8. Astrophysics

Just find v(5)

9. anonymous

okay so then v(5) = -2

10. Astrophysics

Yes

11. anonymous

okay and for the speed i just find s(t) and plug five into that right?

12. Astrophysics

s(t) is the position

13. Astrophysics

speed is just scalar

14. anonymous

okay so then speet(t)=2 ?

15. Astrophysics

Yes, speed is just the magnitude or the velocity

16. anonymous

okay lovely ! thank you very much!

17. Astrophysics

Yw :)

18. Astrophysics

We could find the position to s(t), by integrating, $v(t) = t^2-9t+18 \implies \frac{ ds }{ dt } = t^2-9t+18$$\int\limits ds = \int\limits (t^2-9t+18) dt = s(t) = \frac{ t^3 }{ 3 }-\frac{ 9t^2 }{ 2 }+18t+C$