Finding Position Function with Initial Position of 5 and v(t) = 5t1/3

[char808]

Homework Statement

Find the position function with the given initial position.

v(t) = 5t^1/3 s(0)=5

Homework Equations

The Attempt at a Solution

Find the anti derivative

15/4t^4/3 + c

s(0) = 15/4t^4/3 + c
5 = 0 + c I'm assuming since s(0) = 5 I just substitute 5 for s(0) here
c=5


s(t) = 15/4t^4/3 +5

 

[rock.freak667]

Yes that is correct.

 

[char808]

So if s(1) = 10s(1) = (15/4)(1)^4/3 + c
10 = 15/4 + c
c = 25/4

(just trying to clear up my understanding of these types of problems. thank you for the help.)

 

[rock.freak667]

So if s(1) = 10


s(1) = (15/4)(1)^4/3 + c
10 = 15/4 + c
c = 25/4

(just trying to clear up my understanding of these types of problems. thank you for the help.)

Yep.