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Does traveling fast as possible shortening the duration of the mission lessen chances of collision or mechanical failure, or does traveling slower in space in some way safer?

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Faster travel is generally better: less time for random or wear-down mechanical failures, less exposure to cosmic rays, lower probability of collisions.

Direction and relative velocity of collisions with meteoroids is highly variable and essentially random. Going faster might make the average impact energy of collisions infinitesimally higher, but not enough to make a measurable difference to safety.

Achieving a significantly faster trajectory, however, requires a more powerful launcher than minimal fuel trajectories.

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Velocity is calculated usually to minimise fuel needed, or sometimes to minimise time - but the time piece is generally about resources/mass, not minimising risk of collisions.

"Safe speed" is pretty much irrelevant until you get up to significant percentages of the speed of light, so your question doesn't really work.

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