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How do you solve this?? pls add your work as well..

How do you solve this?? pls add your work as well..-example-1
User Beasy
by
8.7k points

1 Answer

3 votes

Answer:


(A) - \sqrt2

Explanation:

Let's find the velocity and acceleration first:


v(t) = \dot x(t) = cos\ t -( -sin \ t) = cos \ t + sin \ t\\a(t) = \ddot x(t) = -sin\ t + cos\ t = cos\ t - sin t

(you can also rewrite the position as
\sqrt 2 sin(t-\frac\pi4) and determine velocity and acceleration from there, but I do prefer handling it as a sum for the sake of the derivatives)

At this point, the first time when the velocity is 0 is given by


cos\ t + sin\ t = 0 \rightarrow cos\ t = - sin t \rightarrow tan\ t = -1 \\t = \frac34 \pi = 2.36s

At this point the acceleration is (let's use the first value of t for the sake of our sanity!)


cos (\frac34 \pi) - sin \frac 34 pi = -\frac1{\sqrt2} -\frac1{\sqrt2} = \sqrt 2 = -1.41

User Tahjid Ashfaque
by
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