## pratu043 Group Title 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. one year ago one year ago

1. shamim Group Title

i m trying to solve this problem

2. shamim Group Title

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

3. shamim Group Title

$W=FS=maS$

4. shamim Group Title

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

5. shamim Group Title

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

6. shamim Group Title

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

7. shamim Group Title

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

8. shamim Group Title

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

9. shamim Group Title

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

10. shamim Group Title

or, W=1125 joule

11. shamim Group Title

r u following me

12. Vincent-Lyon.Fr Group Title

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.