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Problem 67

A particle moves along the $x$ -axis at a velocity of $v(t)=1 / \sqrt{t}$ , $t>0 .$ At time $t=1,$ its position is $x=4 .$ Find the acceleration and position functions for the particle.

Answer

$$

\begin{aligned} x(t) &=2 \sqrt{t}+2 \\ a(t) &=-\frac{1}{2 t^{\frac{3}{2}}} \end{aligned}

$$

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## Discussion

## Video Transcript

67 We're looking of velocity function be of TV equal one on this we're which means the glossies of prime. So it's already at every prime To get for position function, we would have to take the integral. So we're gonna call that except Pete. And that is really t to negative 1/2. So what I integrate that when you grow up, I'm gonna get team. I had one Could be a positive one hand and I multiply the coefficient by the gruesome body expert too. Let's see. So accept t x t He's the 1/2 which is where we see And if I see we're getting you back that we know Oh, the position is poor when x is home. So I have to spirits of one. Let's see, it's weird one one times two of seeing s t. So my position function Okay. Hey, 2222 teams two My position function and find my acceleration function and take the derivative of velocity. So you take with him. Yeah, the derivative of the velocity be double prime of tea, which is also the same thing as acceleration. About teen. He calls, um negative one and plans but key negative three because it's a track one from you

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