What is the Acceleration of a Vehicle at Different RPMs?

[Triple88a]

Homework Statement

Find the Acceleration of a vehicle at 3k rpm and 5k rpm.
At 3k the engine produces 65hp. At 5k it produces 155hp.
Car weight is 1000kg. The wheels are 50cm in diameter. The engine is connected to the wheel via 2:1 ratio transmission. Neglect any losses.

Homework Equations

kW = HP*0.7457 Nm (torque) = (kW*9550)/RPM
Total Newtons =Nm*(Gear ratio) / Tire Radius in meters
Acceleration: MA = F ... Total Newtons / Car weight.

The Attempt at a Solution

kW = 65*.7457 = 48kW 48*9550/3000 = 154Nm (torque at 3k rpm)
154Nm*2/.25m = 1232N
MA= F... F/M = A 1232N / 1000 = 1.232MS^2 but for some reason that doesn't seem right. Others are getting different results so I'm not sure whos wrong.

The 5k is the same formulas so no point of posting that as well.

Thanks for reading.

 

[billy_joule]

Looks like you forgot to account for the transmission ratio.

 

[Triple88a]

Looks like you forgot to account for the transmission ratio.

The Transmission ratio is the 2nd number.

154Nm*2/.25m = 1232N 154Nm * 2 since 1:2 tranny doubles the torque / the leverage of the tire. No?

 

[billy_joule]

The Transmission ratio is the 2nd number.

154Nm*2/.25m = 1232N 154Nm * 2 since 1:2 tranny doubles the torque / the leverage of the tire. No?

Ah, I missed that. In that case I'd agree with your answer.

The engine is connected to the wheel via 1:2 ratio transmission.

I guess this could be interpreted (incorrectly IMO) as:
engine:wheel = 1:2
Which results in a ridiculous road speed of 942 km/h @ 5000rpm

 

[haruspex]

For what it's worth, I get the same answer by a different route.
3000rpm=50rps, or 25rps at the wheels.
25π0.5=39m/s (about 140kph)
F=P/v=48kW/39m/s=approx 1200N.

 

[Triple88a]

Is the Acceleration in M/S2 correct?

 

[haruspex]

Is the Acceleration in M/S2 correct?

making my calculation in post #5 a little more accurate, 1230N. 1230N/1000kg=1.23m/s².