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If we find the force for a decelerating object (let's say a car on a road), we'll see that the force is negative as in it’s in the opposite direction of the motion of the object. I wanna know what this means. I'm still finding the force from the object (because the mass and decelaration is of the car), so does this mean the object (car) is applying a force on the road in the opposite direction of its motion? But how? (I read somewhere that this is the resistive force of the road on the car. Again how's that possible, I'm finding the force for the car, NOT the road) Please provide details.

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    $\begingroup$ FWIW: In reality, forces are 3-D vectors -- mathematical quantities that have an unsigned magnitude (a.k.a., "length") and an arbitrary, 3-D direction. But, for problems where the motion and the forces are all constrained to the same straight line, there are only two possible directions. That enables us to take a short cut: Instead of using full-on vectors, we can just use a signed number where the absolute value of the number represents the vector's magnitude, and the sign, "+" or "-", tells us which of the two possible directions. $\endgroup$ Sep 16 at 13:36
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If we find the force for a decelerating object (let's say a car on a road), we'll see that the force is negative as in it’s in the opposite direction of the motion of the object.

Not necessarily. The sign of the force just depends on its direction; it has nothing to do with the direction of motion of the object. If the object is moving in the positive direction, but its speed is decreasing, then we can conclude the net force is in the negative direction. However, if the object is moving in the negative direction, but its speed is decreasing, then we can conclude the net force is in the positive direction. In either case, a "deceleration" is happening, but the force could be in either the positive or negative direction.

I'm still finding the force from the object

If you are looking at the motion of the object, then you are looking at forces acting on the object. Of course, you can relate these to forces the object exerts by Newtown's third law, but these forces could be acting on different things.

so does this mean the object (car) is applying a force on the road in the opposite direction of its motion? But how?

If a car has its breaks applied a force (or it might be easier to say a torque) is applied to the wheels. In turn friction between the wheels and the road causes the car to slow down. Note that this process is completely independent of what we have called "positive" and "negative". As the previous example (hopefully) showed, there isn't anything special about a "negative force" vs a "positive force".


To answer your title question. A negative force is one that acts in the negative direction based on how you have defined your coordinate system. Note that this really only makes sense in one dimension. In multiple dimensions it doesn't make sense to say "negative force", since "negative" isn't unique. It's always best to talk about directions, since this generalizes very well. So in your case you are really asking about forces in one dimension that act in the negative direction. This doesn't mean there is anything special about the force; it's just giving its direction.

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There's a few pieces to this. The first is that it will be easier to understand forces if you don't think of them as "negative." Forces are vectors, which have a (positive) magnitude and a direction.

Where you can get a "negative" thing regarding vectors is when you write them down in component form. When using components you pick which direction is the positive x direction, and which direction is the positive y direction, and if the vector is in the opposite direction, this yields a negative number for that component. The vector as a whole has no concept of negative, but it may have some negative numbers when you look at it in components.

Later on, you will learn about work. Work is a number which is negative if the force and velocity are in different directions. So your intuition that there's something negative-ish about this situation is correct. You'll just learn about work and energy later. For now, we're just talking forces and velocities.

Phrasing aside, I think the core of your question is:

... the force is ... in the opposite direction of the motion of the object. I wanna know what this means.

It actually doesn't mean much more than you already understand. Fundamentally, we know that objects can have an acceleration in the opposite direction of their movement. We call that deceleration. Given that the force is defined via $F=ma$, logically the force must be in the direction opposite of the movement as well. It doesn't have any deeper meaning than that. If the force is in the opposite direction from the velocity, it just means the object id decelerating.

... does this mean the object (car) is applying a force on the road in the opposite direction of its motion?

No. If there is a force applied to the car by the road which is in the opposite direction of the car's velocity, then Newton's third law states that there must be a force applied to the road by the car that is equal and opposite. Thus the force applied to the road by the car is in the same direction as the velocity of the car.

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A force (F) is a vector quantity. A vector has a magnitude (which cannot be negative) and a direction. The negative of (F) is a different vector with the same magnitude but opposite in direction. When working with vectors, it is usually best to work with their components. In a chosen coordinate system, a vector may have one or more negative components which point in the negative direction of the corresponding axis. When working a problem in one dimension it is easy to forget that you may be working with components of vectors.

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When you apply brakes to a car the rolling motion of wheels is reduced. In day to day life you might have seen that a rolling body rolls farther than a body slipping this is because ground applies a resistive force to the slipping body but it applies no torque in the forward direction this causes the body to stop faster. Same thing happens when brakes are applied the torque applied by resistive force due to ground is counterbalanced by the friction between the brakes and the tyre so the resistive force applied by ground decelerates the body faster. Note that if brakes are not applied the car will still slow down unless you hit the accelerator.

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does this mean the object (car) is applying a force on the road in the opposite direction of its motion? But how?

Yes, it does. The forces the brakes exert on the wheels cause them to turn more slowly, and that in turn causes them to pull on the surface of the road, and that pulling force will exert a backward force on the car (slowing the car down) and an equal and opposite force on the road (slightly stretching the material of the road in contact with the tyres in the direction of travel). Of course, when understanding braking, it's important to keep in mind that the point on the tyre where the tyre touches the road isn't moving relative to the surface of the road, in order to maximize the force of friction between them.

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Regardless of whether the the object is accelerated or decelerated, if there is a force in one direction, then there is also a force in the opposite direction. This is Newton's 3rd law.

When your car speeds up (positive acceleration), then its engine applies a torque about the wheel axles, which forces the wheels to rotate faster. This would cause sliding with the surface if we didn't have static friction. The static friction force pushes backwards in the ground. As per Newton's 3rd law, this same static friction force pushes forwards in the car. You can think of it as the car "pushing itself away from the ground". This forwards force causes the acceleration.

When slowing down (deceleration, negative acceleration), the brakes of the car apply an opposite torque to the wheels forcing them to rotate slower. This would again cause sliding (if the car continued moving with stationary wheels), but again static friction again prevents such sliding. This time it points in the opposite direction, though, so forwards in the ground and thus per Newton's 3rd law backwards in the car. This backwards static friction force is what causes the deceleration.

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