# Acceleration of a vehicle

#### Triple88a

1. The problem statement, all variables and given/known data
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.
2. Relevant 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.

3. 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 doesnt 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.

Last edited:
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#### billy_joule

Science Advisor
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

Science Advisor
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

Science Advisor
Homework Helper
Gold Member
2018 Award
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

Science Advisor
Homework Helper
Gold Member
2018 Award
Is the Acceleration in M/S2 correct?
making my calculation in post #5 a little more accurate, 1230N. 1230N/1000kg=1.23m/s2.

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