If the acceleration of an object is given by dvdt 2v find...

Transcript

00:01 In this case they give us a differential equation for the acceleration object.

00:04 They give us dv and d t is equal to minus 2v.

00:10 So we're going to separate the variable so we're able to integrate.

00:14 Dv is going to be dv over v is going to be equal to 2dt.

00:19 Then we can integrate both sides.

00:22 Here we're going to get the natural log of v, absolute value of v that is, and it's going to be minus 2t, plus.

00:30 A c that we should figure out and the first thing we need to figure out is that c that so they give us an initial value when velocity is at times zero is seven so we we plug in this right away ln of 7 is equal to 0 plus c so from here we know that c is equal to ln of 7 and we're gonna just put just 7 because we don't need the absolute value the absolute value of 7 and 7 so so now we have the the question of ln of v is equal to minus 2 t plus ln of 7 now maybe we need to solve this for for v so because we want to find the they want to find the position so we know kind of have to integrate again so assuming v is positive we're going to find that v is equal to e to the minus 2 t plus ln of 7 which is the same as saying 7 e to the minus 2 t because here e to the ln of 7 is 7 so and we can check that when when t is equal to 0 this gives 7 for velocity now we're assuming that velocity is is maintaining itself positive otherwise we're going to have to be a little more careful with the with this little detail right here.

02:12 So then we're going to integrate again to get to find a position.

02:17 So to find the position, the position s is going to be equal to the integral of 7e to the 2d...

Question

If the acceleration of an object is given by dv/dt = -2v, find the position function s(t) if v(0) = 7 and s(0) = 0.

Question

If the acceleration of an object is given by dv/dt = -2v, find the position function s(t) if v(0) = 7 and s(0) = 0.

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