# The most basic question re: acceleration, velocity, and force

1. Jun 26, 2009

### 2clients

Hello,

So I know F = ma. If a particle is moving at constant velocity and strikes something, doesn't that mean there will be zero force, beacuse there is no acceleration? I'm having a hard time conceptualizing this, as it seems there would be a large force. For example, if a bullet could somehow travel at a constant velocity, how would there be no force upon striking something?

When is it possible for something with mass to have zero acceleration?

Thank you.

2. Jun 26, 2009

### Staff: Mentor

No. If the particle strikes something, it will experience a force and thus an acceleration.
Sounds reasonable to me!
If a bullet strikes a wall, there will be plenty of force and acceleration.
When the net force on it is zero. Rest it on a table, for instance.

3. Jun 26, 2009

### 2clients

Thank you Doc Al!

How about a bullet that is moving through the air at a constant velocity. Is that a force?
If so, how does it fit into F= ma?

4. Jun 26, 2009

### Tac-Tics

You have to remove yourself a little from the complexities of everyday life in studying physics. Considerations like friction, wind resistance, or laziness on the part of the experimenter must be ignored.

Of Newton's three laws, the first is the hardest to accept. It says that things moving at a steady pace try to keep moving at a steady pace.

Take a bowling ball, for example. Your hand speeds it up and you let go of it. From the time it leaves your hand to the time it strikes the pins at the other end, it moves in a straight line at a constant speed. We call this tendency for things to move like this "inertia". It's very important!

Another example is the pull you feel while driving in a car as you turn the corner. When a car makes a right hand turn, you feel pulled towards the left. This is because your body and everything in the car wants to keep going in a straight line, even though the car is NOT going in a straight line.

In your bullet example, you seem to have misunderstood how to use the equation F=ma. Let's work out that scenario.

When a gun is fired, a large force is applied to the bullet that causes it to speed up tremendously. Like the bowling example above, the bullet moves at a constant rate (with zero acceleration) after it leaves the barrel. However, once it strikes a target, the bullet stops! It goes from a large velocity to zero velocity, and that's the acceleration you would use in the equation.

If you think about it, it makes sense. While the bullet is flying through the air, it's not pushing against anything. It's just doing what it likes to do and the man it's traveling at is minding his own business. It's only once the bullet strikes the man that either party feels the effects.

5. Jun 26, 2009

### 2clients

Thank you Tac-Tics!

6. Jun 26, 2009

### 2clients

Last question:

When is it possible for something with mass and velocity to have zero acceleration? It seems there has to always be some infinitessimal change in velocity, therefore having velocity means having acceleration?

7. Jun 26, 2009

### Staff: Mentor

If the bullet's moving at constant velocity, then the net force on it is zero. But velocity itself is not a force.
Having a velocity does not imply having acceleration. As a practical matter, it might be nearly impossible to eliminate or control all sources of interaction (and thus force) to maintain an exactly zero net force. But that's just a practical matter, not fundamental to understanding F = ma.

8. Jun 26, 2009

### 2clients

Okay! Thanks again very much!

9. Jun 26, 2009

### Tac-Tics

2clients - Have you taken any calculus? The relationship between position, velocity, and acceleration is the first thing you learn.

Suppose you have a ball. It moves over time. For any point in time, it is in exactly one place. We can plot the position of the ball at different points in time. The x-axis represents time and the y-axis represents position.

We call the position the ball at time t by the name of x(t). So if x(0) is where the ball is right now, then x(10) is where the ball is 10 seconds from now. The net distance the ball traveled in that time is whatever the value of x(10) - x(0) is.

Take any point in time and call it t. We know that x(t) is the position of the ball after t seconds. Choose a very, very small amount of time called dt. So x(t + dt) is the distance just a split second after t seconds. It shouldn't be much bigger or smaller than x(t), but it won't be exactly equal either.

The velocity of the ball at time t is the quantity $$\frac{x(t + dt) - x(t)}{dt}$$ when dt is extremely small. This formula is actually a formula for the derivative of the function x. Derivatives are super important in physics.

10. Jun 26, 2009

### 2clients

Tac-Tics - thank you very much for the additional explanation. I've taken three semesters of calculus up to multivariate calculus and two semesters of physics. I rememeber learning that velocity is the first derivative of position and that acceleration is the second derivative of position and first derivative of velocity, but thanks for the more thorough math review.

I originally had trouble when thinking from a practical standpoint how constant velocity could have zero force, but now I understand much better. This all started when I wrongly told my friend that if we were traveling in a car at a constant speed, we wouldn't have any force because we have no acceleration. Now I understand better, and it's my understanding that because there are almost always non-conservative forces present on Earth, there can in practical terms never be constant velocity on Earth. With that said, having a velocity somehow is not supposed to imply having an acceleration!

Last edited: Jun 26, 2009