# Why don't cars accelerate according to F = ma?

• B
• tharindu_
tharindu_
TL;DR Summary
why a car with a constantly running engine maintains a constant speed instead of continuously accelerating?
If the engine is constant, then the wheels of the car exerts a constant force on the floor. And F = ma, So the car should be accelerating rather than maintaining the same speed.
What is going on here?

tharindu_ said:
What is going on here?
Acceleration only happens if the sum of all forces is not zero. As you note, the car does not accelerate even though the engine is applying a force. What other forces might be at work?

OmCheeto and tharindu_
tharindu_ said:
TL;DR Summary: why a car with a constantly running engine maintains a constant speed instead of continuously accelerating?

If the engine is constant, then the wheels of the car exerts a constant force on the floor. And F = ma, So the car should be accelerating rather than maintaining the same speed.
What is going on here?
Interestingly, that was what everyone thought before Newton. That it takes a force to maintain constant motion. And, in the absence of a propelling force, objects will naturally slow down. The motion of the Moon and planets around the Sun were explained by the "hand of God" providing the propelling force.

Newton changed that. He recognised that objects would naturally continue to move without a propelling force. But, that on Earth, it was impossible to avoid forces of resistance that gradually slowed things down.

For a modern example, compare a car that requires a force to keep moving along a road with the Voyager space probe, that will continue to move through empty space at the same speed effectively indefinitely without any means of propulsion.

Demystifier, tharindu_ and sophiecentaur
Welco
tharindu_ said:
TL;DR Summary: why a car with a constantly running engine maintains a constant speed instead of continuously accelerating?

If the engine is constant, then the wheels of the car exerts a constant force on the floor. And F = ma, So the car should be accelerating rather than maintaining the same speed.
What is going on here?
Welcome, @tharindu_ !

Besides what has been explained above, the torque produced by a car engine depends on its rotational speed.

It increases with the rotation until reaching a maximum value and then decreases.

The gears of a transmission help with that, but it is impractical to have infinite combinations to accommodate higher and higher speeds of the car (assuming constant acceleration could be sustained).

danielhaish said:
Friction is increasing in higher speeds due more collisions between air particles and the car , and those colositons accours in higher speed . Therefore the car stops accelerating in some point even though you keep pressing on the gas and it requires higher force to accelerate
That's not the the key factor. For example, you can only run at perhaps 10 km/h. But, you can still run (more slowly) into a 20km/h headwind. So, that can't be the full explanation. Likewise, you can't run at 30km/h with a 20km/h tailwind.

The same goes for a car. You can't add and subtract the windspeed to determine your maximum speed.

phinds
danielhaish said:
But without the change in the friction, The engine of the car wouldn't have to go faster also when press slightly on the gass pedal would cause the car to accelerate fpr ever. So this maybe may explain why the engine cant turn around faster but also if turn around in the same speed it would have to keep accelerate the car because still you add energy to the system
The real reason is that to maintain a constant acceleration force (even in a vacuum) by pushing on a road, the power must increase, as the kinetic energy of the car increases. With fixed or maximum power output, the accelerating force itself reduces with speed. We have ##P = Fv##. Where ##P## is the power required to generate an accelerating force of ##F## at speed ##v##.

This equation applies even without any resisting forces. If you add even a small resisting force, then this balances the accelerating force at a high enough speed.

PeterDonis
danielhaish said:
But also the vacuum the fact that your'e pushing something means there is friction.
No it doesn't. Resistance to acceleration is called inertia, not friction.

danielhaish said:
But friction is the force applied between to object moving relatively to each other
Not all forces between relatively moving objects are friction. Gravity, electrostatic and magnetic forces are things.

Not all frictional forces are between relatively moving objects. Static friction is a thing.
danielhaish said:
And the answer is the change of the resetance due more colositons in higher speeds
There is more to fluid dynamics than "more collisions". Yes, molecular collisions are at the heart of the underlying explanation. But the emergent behavior does not have the simplistic properties that one might expect. There is a reason that we use airfoils rather than flat plates.

With a "more collisions" model, do you predict linear drag, quadratic drag or something else?

Given a quadratic drag force model, what relationship would you predict for required engine power as a function of steady state velocity?

PeroK said:
That's not the the key factor.
Of course, it is. If there was no resistance, you would always keep accelerating.

PeroK said:
With fixed or maximum power output, the accelerating force itself reduces with speed. We have ##P = Fv##.
But ##F## never goes down to zero, no matter how high the speed is. If you want to stop the acceleration, you need a resisting force of some kind.

Let's not forget the OP's question:
tharindu_ said:
TL;DR Summary: why a car with a constantly running engine maintains a constant speed instead of continuously accelerating?

Last edited:
jack action said:
Of course, it is. If there was no resistance, you would always keep accelerating.
The key point is that even if you reduce resistance to zero, the acceleration drops off quickly as speed increases. I think in this case velocity is proportional to ##\sqrt t##. In practice, you would see something similar to reaching a terminal velocity. Even though, theoretically, velocity would go on increasing indefinitely.

The key point is that the motive force reduces in proportion to speed. It only take small resisting force to cancel out this. This is in contrast to the common view, expressed in this thread, that the motive force remains constant and the reduction in acceleration is due mainly to increased resisting forces.

The key example is cyling with a tailwind. Yes, you can go a bit faster, but even with no wind in your face, you still quickly reach a maximum speed. If what you say were true, then you could add effectively any tailwind to your maximum speed. And with a 30km/hr tailwind, you could do 60km/h on a bicycle. I.e. until the wind resistance gets to effective 30 km/h.

It's also why, although you cannot make your bicycle go any faster, when you stop peddling you can still coast close to maximum speed. Or, in fact, slow down gradually. If what you say were true, then as soon as you stop peddling hard, you would rapidly lose speed, due to the great resistance force. This does not happen, because the resisting forces are relatively small and the lack of acceleration was due to the reduction of motive force with speed at fixed power.

Mister T
tharindu_ said:
If the engine is constant, then the wheels of the car exerts a constant force on the floor. And F = ma, So the car should be accelerating rather than maintaining the same speed.
What is going on here?
The ##F## in your equation is not the force exerted on the floor!

@tharindu_ your original question cannot be answered because you haven't included all the variables involved. Cars are legendary in their property of having no exact simulation yet people have 'faith'. If you want to aim at a fuller understanding of elementary dynamics then you should start with much simpler models - like space rockets and trolleys running down slopes.
The most straightforward statements about motor car performance are much too simplified.

Moreover there are many non-Physicists who hold forth about motor cars on the basis of (rarely, even their own) measurements. Treat most of what you read about the theory of motor cars with suspicion until you understand the basics. Much of it is intuitive and even some actual measurements can be misleading (faith, again).

But, of course Motor Cars Are Fun.

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