## Denebel 3 years ago an automobile accelerates from rest at 1+ 3* sqrt (t) mph/sec for 9 seconds. What is the velocity after 9 seconds?

1. 14yamaka

1+3sqrt(9) 1+3(3) 1+9 10mph

2. Xishem

^ Wouldn't this find the acceleration at time t, not the velocity?

3. Xishem

*time 9s

4. 14yamaka

Good point Xishem... I wondered about that too, but I can't tell from the question X(

5. Xishem

Would integrating the function from 0 to 9 give the correct answer?

6. mattt9

yes

7. Denebel

Hm, when the problem states it like that... does it mean that the velocity is the function 1 + 3*(t) or the acceleration?

8. mattt9

the function is of acceleration

9. mattt9

so its integral will be velocity

10. 14yamaka

It means acceleration....yeah, Xishem, you're right, this will require integration

11. Denebel

Yeah, the book says mph/sec.. how should it be stated if it was giving the velocity?

12. mattt9

(t+6t^(3/2)) from 0-->9

13. mattt9

i would change either the hours to seconds or vice versa

14. mattt9

15. mattt9

this can be done by dimensional analysis

16. dumbcow

i get v(t) = t + 2t*sqrt(t) v(9) = 9 +2*9*sqrt(9) = 63 mph

17. Denebel

integral of sqrt (t) = [2t^(3/2)]/3 Multiply that by the 3 constant.. = 2t^(3/2) am I doing something wrong? I can't get sqrt (t)

18. mattt9

it's the same thing... 2t*t^(1/2)=2t^(3/2)

19. Denebel

Oh I see. I would have never though of to do that... makes calculations so much easier, haha.