Question

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

Answer 1

`(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`