Q18 of 26 Page 17

A particle executes the motion described by X(t) =X0(l - e-yt) t ≥ 0,

(a) Where does the particle start and with what velocity?


(b) Find maximum and minimum values of x (t), v (t), a (t). Show that x (t) and a (t) increase with time and v (t) decreases with time


x(t) = x0( 1 – e-yt)

(a) The particle starts at t = 0 that is at x = 0.


For velocity, we need to differentiate the given equation with respect to time.




At t = 0, v = . This is the starting velocity of the object.


(b) x(t) will be maximum when ‘t’ approaches infinity and will be equal to x0. It is increasing from zero to x0 with time.


v(t) will be maximum at t=0 and will be x0y. It will be minimum as ‘t’ approaches infinity. Clearly it is decreasing with time.


a(t) will be maximum as ‘t’ approaches infinity and will be equal to 0. Its minimum value will be (–x0y2) at t = 0. We can note that acceleration is increasing (from (–x0y2) to 0) with increasing time.


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