Question

please submit the response if ypu are sure the answer is correct.

3. The velocity of a given object is determined by ** = -kv”, k > 0,n 20 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) If13n< 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

dv kso, no at Vo) = Vo . = -K at in Close I if nel = -kt te nt - + + + V -nti so vln Inn xt & Vor -Rt + In In soif v=o then kt = Volon Since I-nzo for n</ T-n t= Von Klin) so object come to rest at finite time For maximum distance 1x=0 ) V=0 at t=vo" K(1-1) 2 1.

v=dx where d = vin gth = (-xt + a) (ln) fv = f(-xt Fillington * = (in fon (+*+ +x) + c (0) = 0 0 = (1-ngen (a 80 c = + (1-18m (2 hora y n (02/10 x = (langin (-kt+Q) F as t= Voln K(1h) x= (1-ngton () 2 / 2 v Kle when a vo