Doubt on Power, Torque and RPM

Power=Jule /second

Jule=Newton*Meter

So power= NM/sec

NM= Torque

Power= torque/sec

Power=torque*rpm

This shows that when rpm increases torque decreases.

This shows that when rpm increases torque decreases.

Or possibly even that Power increases???????????

But when vehicle climbing up why we need more torque -

More torque is required to give more power since you are working against gravity.

and As r.p.m increases,The torque increases up to certain value and then decreases

As you press the accelerator, more fuel is pumped into the engine, the engine power obviously increases, till it reaches its limit. Then the load power tries to overcome it (since you are at high gear and hence high RPM and the combined power required- potential+ kinetic is more than the engine can supply even at the full fuel feed and it now splutters. You reduce the RPM, the KE goes down as well as the PE (or rather Potential power) and the engine may be able to take this.

why clutch will be placed in between Engine and Gear box - Engine has to run. You want the minimum components along with it to run when not necessary.

Thank you very much sir