# Physics Question, Push and Drag on a car

I was wondering, if the force that causes a car to move in one direction is matched by the drag force opposing in the other direction, why does the car move at a constant velocity rather than moving at zero velocity. I thought that when one force opposes the other equally, there is no net movement. Please help, thank you.

Ah, I understand what you mean. I was quite confused by this very same thing when I first encountered it. Enough chatter, I'll get straight to an answer.

You seem to be confusing equal and opposite forces, and acceleration. This is a classical matter of physics that fits well within the framework of Newtons laws, namely newtons first law. which states: (loosely)

That a body in motion will stay in motion, and a body at rest will stay at rest, unless acted on by an outside force.

If you look at the second law now which is simply the mathematical statement

F = ma (we'll stick with the simplest form here)

It simply states that a force is felt when there is acceleration.

Newton's third law which states,

For every action there is an equal and opposite reaction.

What you are missing is here in Newton's third law.

There is a force and a reaction force which cancel each other out.
Therefore, by the first law, the body should continue in it's same direction without any change because there is no acceleration present to enact a force.

Assuming there are no relativistic effects, i.e. velocities appreciable to the speed of light, that's the description you are looking for. I figure this is about what you are asking for correct?

CWatters
Homework Helper
Gold Member
I thought that when one force opposes the other equally, there is no net movement.
No thats not correct. When the forces balance there is no acceleration but there can be movement.

For example a space craft travelling to mars does not have to burn it's engine all the way there. During the cruise part of the flight it speeds along with the rocket switched off so the force acting on the rocket is zero...yet it's still moving through space.

Consider your car starting from a standstill. Initially the force due to air drag is zero (it's not moving through the air). As the car accelerates the drag forces increase until they match the thrust provided by the engine. At that point the forces balance and the car cannot accelerate any more...but it can still continue at a constant velocity.

As rethipher says the relevant equation is F=m.a

If the total Force F=0 then the acceleration a=0 but velocity doesn't figure in the equation so can be anything. What the velocity can't do is change because changing velocity is acceleration.

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Thank you guys for all your help!