`v(t) = 1.5sqrt(t), s(4) = 10` A particle is moving with the given data. Find the position of the particle.

Textbook Question

Chapter 4, 4.9 - Problem 60 - Calculus: Early Transcendentals (7th Edition, James Stewart).
See all solutions for this textbook.

1 Answer | Add Yours

shumbm's profile pic

Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

Posted on

As I understand we have to find s(t).

`s(t)=int(v(t))dt=int(1.5sqrt(t))dt=1.5*(2/3)*t^(3/2)+C=t^(3/2)+C,`

where C is any constant.

Also is given that s(4)=10, so `4^(3/2)+C=10,` `C=10-4^(3/2)=10-2^3=2.`

The answer: `s(t)=t^(3/2)+2.`

We’ve answered 318,979 questions. We can answer yours, too.

Ask a question