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A few factors affect may acceleration but we'll stick to the broadest generic ones:
Power to weight ratios
Is the amount of power that the engine has over the weight of the vehicle. I'm sure you can understand that a smaller engine with a smaller vehicle mass would fare better on accelleration than a larger engine with a huge weight. Thus the better option is to have a smaller body and lighter parts being powered by a larger motor.
A Formula One vehicle has a great power to weight ratio, so do most modern superbikes and they both accelerate at alarming speeds.
Traction
A large power to wight ratio, ie a large engine with a smaller body is not always a recipe to success. Adequate traction has to be considred. That's why formula one adn other racing vehicles have such broad tyres for their relatively light bodies and fantastically powerful motors.
Consider Drag racing. The two components most notable are large tyres with a huge engine!
if you're looking for more; a more detailed description, of what affects a specifc vehicle and it's acceleration, would have to be discussed after a more detailed question.
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force and acceleration
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smooth paved surfaces
