anonymous
  • anonymous
The speed of a cycle increases from 2.5 m/s to 5 m/s. The total mass of the cyclist including the cycle is 120 kg. Calculate the work done by the cyclist to increase the speed.
Physics
katieb
  • katieb
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shamim
  • shamim
i m trying to solve this problem
shamim
  • shamim
here u=2.5 v=5 m=120kg work done W=?
shamim
  • shamim
\[W=FS=maS\]

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shamim
  • shamim
again we know\[v ^{2}=u ^{2}+2aS\]
shamim
  • shamim
\[or, 2aS=v ^{2}-u ^{2}\]
shamim
  • shamim
\[or, aS=\frac{ v ^{2}-u ^{2} }{ 2 }\]
shamim
  • shamim
putting this value of aS in the 1st equation we get
shamim
  • shamim
\[W=m(\frac{ v ^{2}-u ^{2} }{ 2 })\]
shamim
  • shamim
\[or, W=120 \times (\frac{ 5^{2}-2.5^{2} }{ 2 })\]
shamim
  • shamim
or, W=1125 joule
shamim
  • shamim
r u following me
Vincent-Lyon.Fr
  • Vincent-Lyon.Fr
Use work-energy theorem, and write: \(W=m(\Large\frac{ v ^{2}-u ^{2} }{ 2 })\) directly. This is more general than the derivation provided by shamim, as it will be true even for non-uniform acceleration. But this will only be true if the cyclist is on a horizontal road.

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