Finding horsepower for go-kart acceleration and steering rod lengths

[tower]

I am designing a go kart for my college project. I am stuck with finding out how much horsepower I need. I know the centre of gravity and the total weight. Say I set a criteria that the gokart has to accelerate at some m/s^2 from there on how can I find the horsepower. I know the tyre radius and the ratio in the chain and sprocket, so I can find out the rpm I need at maximum speed. I am going to use an electric motor.

Another thing is when you talk about a motor rated at for example 5 horsepower 1500 rpm does that mean that it has that hp at all rpm and 1500 is the maximum rpm?

And I am totally lost on calculating the lengths of the push rods for the steering.

 

[Danger]

Welcome to PF, Tower.
To start with, there are no push-rods involved in steering. Those are the connecting links between the lifters and the rocker arms. You might be thinking of tie-rods, which connect the two steering wheels to each other.
I have no idea about this 5-hp stuff. The only go-cart that I ever saw had two 750 Kawasaki engines—one driving each rear wheel. It topped out at about 150 mph.

Then there was Fred Goeske's cart...
Normal itty-bitty go-cart, with itty-bitty wheels and tires, and an itty-bitty seat... with a 10,000 hp peroxide rocket on the back. On the quarter-mile track, he gave one second of thrust on the line, 1/2 second at mid-track, and went through the traps at over 250 mph.

 

[DyslexicHobo]

Welcome to PF, Tower.
Then there was Fred Goeske's cart...
Normal itty-bitty go-cart, with itty-bitty wheels and tires, and an itty-bitty seat... with a 10,000 hp peroxide rocket on the back. On the quarter-mile track, he gave one second of thrust on the line, 1/2 second at mid-track, and went through the traps at over 250 mph.

So that's why they call you 'Danger'.

 

[Danger]

Jeez, no! I didn't drive the thing.
I like speed, but in something a bit more controllable. Fred went sideways through the traps one time and broke his back. He was back racing the next season, but stuck with the dragster and funny car.

 

[Topher925]

Another thing is when you talk about a motor rated at for example 5 horsepower 1500 rpm does that mean that it has that hp at all rpm and 1500 is the maximum rpm?

That means that at 1500 rpm you will be outputing 5hp. ICEs have terrible power curves and don't generate much power at all when at lower rpms.

The total amount of power you will need is the equal to the power required to accelerate the cart (perhaps uphill), plus rolling resistance, air resistance, and losses in the drive train. The parameters of your engine depend highly on your transmission. Matching and engine to a transmission is not a trivial task and can be rather complicated. It is a lot easier to first find your engine, then your buck, and from that determine your transmission ratios.