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A particle is moving with the given data. Find the position of the particle.

$ a(t) = 3\cos t - 2\sin t $, $ \quad s(0) = 0 $, $ \quad v(0) = 4 $

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$$s(t)=2 \sin t-3 \cos t+2 t+3$$

01:56

Wen Zheng

01:53

Amrita Bhasin

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Derivatives

Differentiation

Volume

Missouri State University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

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In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

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For this problem, we're starting off with an acceleration function. Three co sign t minus two. T f t equals three. Sign t minus two. Okay, that means that our velocity function is going to be the anti derivative of those. So we're going to end up getting three sign T plus to co sign antique. Classy. But we know that via zero is four. So based on that, we see that C is going to be too. Then we want to find the position function as a T I think equal to the anti derivative of these components. So we'll have uh to 70 yeah minus three coats. Mt us to T. That's our constant. Loving to the constant. You get three. So this is our final position function.

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