Final answer:
To determine the time it takes for a particle to cross the origin, you need information about the particle's initial conditions and equations of motion. Unfortunately, this information is not provided in the question, making any answer speculative.
Step-by-step explanation:
Without the specifics of the particle's initial conditions, position, velocity or corresponding equations of motion, it is impossible to accurately determine the time it would take for the particle to cross the origin. Normally, this information can be obtained from either explicitly given initial conditions or an equation representing the particle's trajectory. Then you would set the position equal to zero to solve for the time particle crosses the origin.
Unfortunately, as the question's details are inadequate, any choice between options a) 1.43 s b) 1.67 s c) 2.14 s d) 2.86 s would be pure speculation.
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