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.

Question

shamim · Answer

i m trying to solve this problem

shamim · Answer

here  u=2.5
         v=5
         m=120kg
work done  W=?

shamim · Answer

$$W=FS=maS$$

shamim · Answer

again we know$$v ^{2}=u ^{2}+2aS$$

shamim · Answer

$$or, 2aS=v ^{2}-u ^{2}$$

shamim · Answer

$$or,  aS=\frac{ v ^{2}-u ^{2} }{ 2 }$$

shamim · Answer

putting this value of aS in the 1st equation we get

shamim · Answer

$$W=m(\frac{ v ^{2}-u ^{2} }{ 2 })$$

shamim · Answer

$$or, W=120 \times (\frac{ 5^{2}-2.5^{2} }{ 2 })$$

shamim · Answer

or, W=1125 joule

shamim · Answer

r u following me

vincent-lyon.fr · Answer

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.