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Suppose that at time ` t ul( gt)0` the position of a particle moving on the x-axis is `x=(t-1)(t-4)^(4)m`. (a) When is the particle at rest ? (b) During what time interval does the particle move to the left ? (c) Find maximum velocity of particle while moving to the left. |
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Answer» `(a) (dx)/(dt)=(t-4)^(4)+4(t-4)^(3)(t-1)=0` `:. " " (t-4)^(3)[t-4+4t-4]=0` `rArr " " t=4s or t=(8)/(5)s` (b) `(dx)/(dt) lt 0 rArr (t-4)^(3)(5t-8)lt0` For this , `tlt 4` and `t gt (8)/(5)` `rArr " " t in ((8)/(5),4)` (c) Particle will be faster when `((dx)/(dt))` is maximum `:. " " (d)/(dt)((dx)/(dt))=0` `:. " " (d^(2)x)/(dt^(2))=3(t-4)^(2)(5t-8)+5(t-4)^(3)=0` `rArr " " (1-4)^(2)[15t-24+5t-20]=0` `rArr " " t=4s " " or" " t=(44)/(20)=2.2s` But at `t=4s(dx)/(dt)=0` `:. ((dx)/(dt))` is maximum at t=2.2 s and maximum value of `(dx)/(dt)=(2.2-4)^(3)(5xx2.2-8)` `=-17.49m//s` |
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