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I am wondering if a car that weighs 2,5kg and a engine power output of 1hp would be just as fast when going in a straight line like a 1250kg car with 500hp (they both would have a weight-to-horsepower ratio of 2,5:1). To make things easier, lets ignore things like efficiency, traction and aerodynamics. Are there other factors I am not aware of?

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If we ignore friction and drag we can revert back to,

One horsepower is equal to 745.7 watts. one watt is 1kg force moving 1-meter per second.

a car with N times power is being pushed by N times force, and assuming it has n times mass

$$F=m\alpha \quad and\ NF=Nm\alpha$$

The answer is yes, the two cars will accelerate with same acceleration.

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Acceleration is determined by power-to-weight ratio. Two vehicles with the same power-to-weight ratio will accelerate at the same rate.

Note however that top speed in level motion does not depend on weight, it depends on another ratio: power-to-drag. Two vehicles with the same power-to-drag ratio will achieve the same top speed- but the heavier one will take more time to get there.

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That is why the power to weight ratio is so important.

As seen on Top Gear, one of the quickest cars around the track is/was the Ariel Atom, as it had a mass of less than 1000kg but relatively lots of power.

Other cars had two or three times the horses but the mass crippled them.

Linear up to a point as other factors come into play - gear ratios and power delivery as well as drag. Tire adhesion also becomes a factor. Then tire flexing etc

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  • $\begingroup$ But that is exactly my question. The weight-to-horsepower ratio in both cars is the same in my question. And my question excludes factors like drag, aerodynamics, gear ratio etc. $\endgroup$
    – MarkAKE
    May 17, 2022 at 12:35
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    $\begingroup$ you didn't answer the question $\endgroup$
    – Tiger Guy
    May 17, 2022 at 13:22

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