I dont understand the motion of this particle

by 404man   Last Updated October 10, 2019 03:20 AM - source I have found the velocity to be equal to $$\dfrac{1}{\sqrt{2}} - \cos t$$ and acceleration to be equal to $$\sin t$$. I am not sure how to find the remaining questions.

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HINT. An object whose position is given by $$f(t)$$ is accelerating if $$f''(t)>0$$ because then its velocity ($$f'(t)$$) would be increasing.

As for the last part, I assume what they mean by 'direction' here is whether the particle is moving 'up' or 'down'. To think what direction the particle is moving, it would be moving in the direction of its tangent line. The slope of the tangent line is given by $$f'(t)$$. So if the particle is moving downward its tangent line has negative slope, i.e. $$f'(t)<0$$, and if it is moving upward its tangent line has positive slop, i.e. $$f'(t)>0$$.

It can also help to compare what you are doing to the actual plot of the particles movement. See this graph here.

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