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A particle moves along the x-axs with the velocity at time t> (or equal to) given by v(t)= -1+ e^(1-t) Find the acceleration of the particle at time t =3. Is the speed of the particle increasing at time t=3? Give a reason for your answer. Find all the values of at which the particle changes direction. Justify your answer. Find the the total distance traveled by the particle over the time interval 0< (or equal to) t< (or equal to) 3.

Mathematics
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