I'm a student preparing for my mathematics finals and I have come across  a calculus related question which has proven to be quite confusing for me So could you kindly explain to me in detail the solution to this problem

Q) A particle moves along a straight line such that it's displacement , X metres, from a fixed point O of the line at the time t seconds is given by X=t-16/t , for t is equal or greater than 1
  A) find the value of t when the particle is at O
  B) The velocity in m/s of the particle when t=5


A) Since X is the distance from O, when is X equal to 0?  That is when the particle is at O.
If 0 = t - 16/t, then 16/t = t, so 16 = tē, so t = 4.

B) To find the velocity when t=5, note that the position is given by X(t) = t - 16/t.
Since velocity is the derivative of distance, this says that V(t) = 1 + 16/tē
Since t=5, V(5) can be seen to be 16/25, or 0.64.  Note that distance is in meters and times is in seconds, so that is 64 cm/s.


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