Question

The velocity of a given object is determined by a = -kv”, k > 0,n > 0 a constant. (This is often used when examining air resistance, but do try to figure out where the method fails.) At t = 0, the object is moving with a positive initial velocity of V, and continues until its velocity reaches zero (if it ever does). (a) Show that the object comes to a rest in a finite amount of time if and only if n < 1 and find the maximum distance travelled in this case. (b) If 1 = n < 2, show that the maximum distance travelled by the object in a finite time is less than (V.2=)/[(2 – n)k]. (C) Show that if n > 2, then there is no limit to the distance the object can travel.

Answer 1

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! (2-0) - This is the distance travelled by object, (b) When 15022 -1 bblLLLLLLI, I, I, I, I, I,,,!! -2 & con # ® < 2- therere, s= Von number : in e S= Vou a finite in a K 2 the particle which is travelled by comming rest. so, the distance will be the maximum distance VO? 2- K (2-n u When a-nco (e) when ny , 2-n so then s becomes infinity if ro in very small, when a-n=0 then also s becomes infinity. Therefore, s hors no limiti G