3 a small object moves along the x axis with acceleration at...

3. A small object moves along the x-axis with acceleration $a(t) = 0.06(20.0-t)$. At $t = 0s$ the object is at $x_0 = -5.0m$ and has velocity $v_0 = 2 m/s$. Determine the x-coordinate of the object when $t = 10.0 s$ and the average velocity from 5 to 10 seconds.

Transcript

0:00 All right, hello.

00:01 In this question, we're given this acceleration equation in the x direction.

00:04 And we're also told an initial position and initial velocity.

00:08 Note i've dropped all the units here because everything is in si, so i don't need to do any conversions.

00:12 And i'll just note in my final answers everything was in si.

00:15 I'm asked, what is the x -coordinate of the object when t equals 10 seconds? so i need to figure out what x of 10 is going to be.

00:23 Well, in order to do that, i'm going to just need to figure out what x of t is going to be.

00:27 So i'm going to need to integrate this function.

00:28 First, i'm going to expand this out just so we have a little bit of a more clear polynomial.

00:34 I'm also going to drop all of the sig figs here, noting that i go to three sig figs at the end.

00:38 And the reason i'm doing that is just to make it nicer and neater to understand.

00:42 So i know that my velocity function, v of t, is the integral of my acceleration function with respect to time.

00:48 So it's the integral of this linear function here.

00:53 Well, taking this antiderivative is simple enough.

00:55 For this, i'm just going to have negative 0 .02t squared.

01:01 And then i need to divide that by 2 so that when i take the derivative, the power or a constant out front stays the same.

01:08 And then plus 0 .2t and then plus some value c1.

01:13 Well, i know that v of 0 is equal to 5 .00...

Question

3. A small object moves along the x-axis with acceleration $a(t) = 0.06(20.0-t)$. At $t = 0s$ the object is at $x_0 = -5.0m$ and has velocity $v_0 = 2 m/s$. Determine the x-coordinate of the object when $t = 10.0 s$ and the average velocity from 5 to 10 seconds.

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