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Solutions to the QUIZ for Sept 25 2008 1 Differentiate y s 2 s2 1 Sol to 1 By the quotient rule dy s2 1 s 2 0 s 2 s2 1 0 s2 1 1 s 2 2s ds s2 1 2 s2 1 2 Using algebra this equals s2 1 2s2 4s s2 4s 1 s2 4s 1 s2 1 2 s2 1 2 s2 1 2 Ans to 1 dy ds 2 s s 4s 1 2 1 2 2 A particle moves according to a law of motion s t2 4t 8 t 0 where t is measured in seconds and s is measured in feet a Find the velocity at any given time t b What is the velocity after 1 second c When is the particle at rest d When is the particle moving in the positive direction e Find the total distance travelled during the first 3 seconds Solution to 2 a v ds dt 2t 4 b v 1 2 1 4 2 In words the velocity after one second is 2 feet per second moving in the negative direction c Setting v t 0 we get 2t 4 0 solving we get t 2 In words the particle is at rest after two seconds d It is moving in the positive direction when 2t 4 0 Solving gives t 2 In words it is moving in the positive direction starting at time two seconds and for ever after e We have to break the journey into two phases From t 0 to t 2 it was moving in the negative direction and since s 2 s 0 22 4 2 8 8 4 it traveled 4 4 during the negative phase From t 2 to t 3 it is travelled s 3 s 2 32 4 3 8 22 4 2 8 5 4 1 So it travelled 1 foot Altogether the distance travelled was 4 1 5 Ans to e The total distance travelled during the first three seconds was 5 feet