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CBSE - IX - Science

Two cars of 1000kg each are travelling with the speeds of 108 KM/H and 72 km/h respectively.
(a)What are their KE?
(b)If their engines are simultaneously switched off, which will travel greater distance if the retarding force acting upon them is same?
(C)What will be the work done in each case?

Asked by vatsalchoudhary41 27th February 2015, 3:31 PM
Answered by Expert

Answer:

begin mathsize 12px style mass space of space the space two space cars comma space straight m subscript 1 space equals space straight m subscript 2 space equals space straight m space equals space 1000 space kg speed space fo space the space first space car space straight u subscript 1 space equals space 108 space km divided by straight h space equals space 108 space cross times 5 over 18 space equals space 30 space straight m divided by straight s speed space fo space the space second space car space straight u subscript 2 space equals space 108 space km divided by straight h space equals space 72 space cross times 5 over 18 space equals space 20 space straight m divided by straight s left parenthesis straight a right parenthesis space Kinetic space Energy space of space first space car comma space straight E subscript 1 space equals space 1 half mu subscript 1 superscript 2 space space equals space 1 half space cross times 1000 cross times 30 space squared straight E subscript 1 space equals space 450 space cross times space 10 cubed space straight J Kinetic space Energy space of space second space car comma space straight E subscript 2 space equals space 1 half mu subscript 2 superscript 2 space space equals space 1 half space cross times 1000 cross times 20 space squared straight E subscript 1 space equals space 200 space cross times space 10 cubed space straight J  space left parenthesis straight b right parenthesis space If space their space engines space are space simultaneously space switched space off space and space retarding space force space acting space upon space them space is space same space which space means space that space retardation space also space same space as space straight F space equals space ma space and space mass space of space both space car space is space same. Using space eq. space straight v squared space minus space straight u squared space equals space 2 as space for space first space car comma space space 0 space minus space left parenthesis 30 right parenthesis squared space equals space 2 as subscript 1 space end subscript left parenthesis space final space velocity space will space be space zero space as space car space is space retarding right parenthesis space straight s subscript 1 space end subscript space equals space fraction numerator left parenthesis 30 right parenthesis squared over denominator 2 straight a end fraction space space space space left parenthesis straight i right parenthesis for space second space car comma space 0 space minus space left parenthesis 20 right parenthesis squared space equals space 2 as subscript 2 straight s subscript 2 space equals space fraction numerator left parenthesis 20 right parenthesis squared over denominator 2 straight a end fraction space space space space space left parenthesis ii right parenthesis from space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis space we space can space say space that space body space which space had space max space speed space will space cover space max space distance space as space the space same space retarding space force space atting space on space them. space left parenthesis straight c right parenthesis space Work space done space equals space change space in space kinetic space energy for space first space car comma space straight W subscript 1 space equals space straight E subscript straight f space minus space straight E subscript straight i space equals space 0 space minus space 1 half mu subscript 1 superscript 2 space equals space 1 half space cross times 1000 cross times 30 space squared space equals space space 450 space cross times space 10 cubed space straight J space space left parenthesis final space velocity space will space be space zero space as space car space is space retarding right parenthesis for space second space car comma space straight W subscript 2 space equals space straight E subscript straight f space minus space straight E subscript straight i space space equals space 0 space minus space 1 half mu subscript 2 superscript 2 space space equals space 1 half space cross times 1000 cross times 20 space squared space equals space 200 space cross times space 10 cubed space straight J space end style
Answered by Expert 28th February 2015, 10:39 PM

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