The misconception that I’ll be talking about today is that a projectile has zero acceleration at the top of its trajectory. It’s a very common question in textbooks and on conceptual tests about physics; a lot of college professors like to ask this in their intro to physics classes. The question is: “What is the acceleration of a projectile at the top of its trajectory?” And normally, students look at it and say “Well, it’s not moving…the acceleration is zero.” But that’s not the case. If an object is not moving and its acceleration is zero, it never will move. So, if the acceleration at the top of the trajectory was zero, the object would go up, stop, and stay there forever. It has to have some acceleration to start moving again. The acceleration of an object in freefall never changes. When the object is on its way up, the acceleration is -9.8 meters per second squared. Negative because it’s pulling down on the object, slowing it down. At the top of its trajectory the acceleration is -9.8 meters per second squared, and on the way down the acceleration is -9.8 meters per second squared because it’s making it accelerate downward. A direction never changes. The magnitude doesn’t change unless the object goes tens of thousands of meters in the air. So, on the way up: -9.8. At the top: -9.8. On the way down: -9.8. So where does this misconception come from? It’s simply the fact that students have a hard time understanding something that’s not moving but still has acceleration. So, you can go through some circumstances with them if we define moving away from us as the positive direction and towards us as the negative direction. We can ask what happens if something is moving away from us and has positive acceleration.
That means it’s speeding up away from us. What if it’s moving away from us as a positive velocity and has zero acceleration? That means it’s moving away from us at a constant speed. What happens if it has positive velocity and negative acceleration? That means it’s moving away from us but decelerating. So what happens if it has no velocity and positive acceleration? That means it’s not moving, but it’s going to start moving away from us momentarily. What happens if it has zero velocity and has negative acceleration? Well, it means that it’s not moving, but it’s just about ready to start moving towards us. So this could be if you have a yo-yo; when the yo-yo reaches the end of its string it has zero velocity, but it’s about to come back up again. Or if you throw a slinky outwards the slinky will stretch and stretch, and eventually it stops. Then the elasticity pulls it back again. So, at its longest length it’s not moving, but it has acceleration back towards us and it will start moving again. Same thing when you throw a ball straight up in the air. If you throw it up with a velocity of ten meters per second…goes 10 9 8 7 6 5 4
3 2 1 0, 1 2 3 4 5 6 7 8 9 10…so, at the top its velocity is zero, but its acceleration is -9.8 meters per second squared. Then you can keep going on with this mental exercise. What happens if something has negative velocity and positive acceleration? That means it’s coming towards us but slowing down. Negative velocity and negative acceleration means that it’s coming towards us and speeding up. Negative velocity and zero acceleration means that its coming towards us at a constant speed. So, it really doesn’t matter which direction you choose…positive or negative. You can choose right, left, up, down, away from, towards… as long as you define it, that’s what’s important. So, there are some demonstrations you can do to show this. You can ask the students to come up with examples of things that have zero velocity but have do have an acceleration, or zero acceleration but do have velocity. You could hold an object in your hand, say, a rubber ball. And when the rubber ball is in your hand it has zero velocity relative to your hand, but it has gravity pulling down on it, so there’s a force on it trying to provide

acceleration. As soon as you move your hand, the object starts to accelerate downward so at the moment that you move your hand it has zero velocity, but it has a downward acceleration, and that’s what causes it to move. Now when the object hits the floor, at some point when it’s hitting the floor it compresses to the maximum amount, has zero velocity, but upward acceleration. And so it will bounce and go back up again.