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Ch 03: Motion in Two or Three Dimensions
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All textbooksYoung & Freedman Calc 14th EditionCh 03: Motion in Two or Three DimensionsProblem 3

Chapter 3, Problem 3

The position of a squirrel running in a park is given by r = [(0.280 m/s)t + (0.0360 m/s2)t2]î + (0.0190 m/s3)t3ĵ. (a) What are υx(t) and υy(t), the x- and y-components of the velocity of the squirrel, as functions of time?

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Welcome back everybody. We have a mole on a farm that is moving with respect to this function or position which is with respect to time. And we are asked to find the X and Y components of the velocity as functions of time. Well, the derivative of position with respect to time is going to equal our velocity which means we are just going to have to take the derivative of the X components and the Y components to find our x and Y components are velocity. So let's go ahead and do that. So the exponent of the velocity is going to be equal to the derivative with respect to time for X component of our position. This is going to be the derivative with respect to time of 0.190 t plus 0.220 t squared Taking the derivative, we get 0.190 plus 0.0440 T says this is the x component. We are going to multiply it by the I unit factor. Great. So now let's go ahead and find the y component of our velocity, Y component of our velocity is going to be equal to the derivative with respect to time of. The Y component of Our position is going to be the derivative with respect time of 0.234 T cubed which is equal to 0.702 t squared. And since it's our Y component we're gonna multiply this by our J unit factor. So now we have found the X component of our velocity in the Y. Component of our velocity, which coordinates to answer choice. Thank you guys so much for watching. Hope this video helped. We will see you all in the next one.
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