Best acceleration torque or horsepower?

[tos001]

i want to ask that in same gear which is true?
a)car accelerates best at the max torque rpm
or
b)car accelerates best at the max horse power rpm

which is true and why
we talk these conditions at same gear
thanks

 

[russ_watters]

Welcome to PF!

Is this homework or an internet argument question or something? Because it is a bit of a trick question.

The acceleration at any instant in time depends on the torque and gear ratio, and the rpm isn't a relevant part of that. So since power is a function of rpm, the power isn't what determines the acceleration: the torque does. So the acceleration is highest at the highest torque.

 

[cjl]

Welcome to PF!

Is this homework or an internet argument question or something? Because it is a bit of a trick question.

The acceleration at any instant in time depends on the torque and gear ratio, and the rpm isn't a relevant part of that. So since power is a function of rpm, the power isn't what determines the acceleration: the torque does. So the acceleration is highest at the highest torque.

The acceleration at any instant depends only on the power delivered and the current speed. Best acceleration at any speed occurs with a gear ratio such that the engine is operating at peak power, not peak torque. For a fixed gear ratio, the acceleration will be best at peak torque, true, but that's because acceleration at a fixed power output is inversely proportional to v² (since power is the rate of kinetic energy increase), and the peak power will always occur at a higher RPM than peak torque.