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Find the velocity and acceleration of a particle whose position function is $x(t)=t^{3}-9 t^{2}+24 t, t>0$

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Chapter 1

Practice Test 1

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Find the velocity, acceler…

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Find the velocity and acce…

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If the position function o…

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The position of a particle…

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00:53

03:24

So for this problem, we can go ahead and start by finding the velocity of our particle. I also know that the velocity is just the derivative of our position function. So to find our velocity, all we need to do is take the derivative of T cute. So we'll move this three to the front and reduce the export of my one. So this is three t squared, minus the derivative of 90 square. Again, we're going to move this tea to the front. So two times nine is 18 times t to the first power and finally plus this 2014. Essentially, we're just going to be the one to the front and we just have plus 24. I'm So now that we have our velocity function, we can find our acceleration function the same way. So we know that since the velocity function is the derivative of the position function, the acceleration function is the second derivative of the position or the first derivative of the velocity. I'm so essentially we know this is the acceleration function, and all we have to do is differentiate this philosophy function. I'm so the derivative of three t squared again. We'll move that to to the front and reduce our power by one. So that's 16 minus. Since we have just a t on the 18 this is just going to be minus 18. And finally, our constant 24 is going to leave us with plus zero at the end. So here we have our velocity function in our acceleration from

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