# Why is acceleration constant in this example?

I was shown this video by our professor: https://www.youtube.com/watch?v=8A7DiGzJUvg&feature=youtu.be

And I do not understand why the acceleration is constant. Our professor told us that a freely falling object has constant acceleration of 9.8 meters per second squared. My first question is if an object is considered freely falling when it is thrown upwards, or if it only becomes "freely falling" when it..actually is falling? Secondly, if acceleration measures the rate of change of the velocity, then from looking at the example in the video, the velocity goes down to 0 when it reaches maximum height. Shouldn't changing from an non-zero velocity to a zero velocity be considered a change in acceleration, since it is slowing down at that time? If I understood this correctly, why is the acceleration constant throughout the video?

At this point I re-watched the video and realized it says "straight line motion" which I'm not sure if they mean a horizontal line [kinda confusing since it is vertical so I feel like it makes more sense to think of it as it being thrown so I guess the question of freely falling doesn't apply, but either way at one point the velocity reaches 0 so why doesn't the acceleration change at all?

The phrase freely falling really means freely moving, that is nothing is pushing or pulling the object while it's moving. So the object is freely falling even when it's rising! Like all things Physics has its own special terminology and I'm afraid you just have to get used to it.

Re the acceleration: the acceleration is the change of velocity with time. If I throw a stone upwards at 98.1 m/s then (ignoring air resistance) in the first second it slows by 9.81 m/s to 88.29 m/s, in the second second it slows by 9.81 m/s to 78.48 m/s and so on until after 10 seconds its velocity has slowed to zero. Each second it slows by the same 9.81 m/s, so the acceleration has the constant value of -9.81 m/sec$^2$ (the - sign means the acceleration is downwards).

• A downvote? Not that I'm fussed, but you need to tell me why you downvoted or I won't know how I can improve the answer. – John Rennie Aug 28 '14 at 9:58

a freely falling object does not have any support to hold it in place and does not have any propulsion.

So, when an object is thrown, the moment that it leaves your hand, it is a freely falling object. This is why there is a change in velocity when you throw it upwards. It slows down to where it reaches a peak and then it speeds up as it comes down.

A straight line motion is just that. Motion along a straight line, the shortest distance between 2 points. Gravity changes that. In a gravity field, the only straight line is when something is rolling across a flat surface. Any freely falling object has only 1 straight line of motion, but it will accelerate along that line.

Look at the velocity plot in that video. It's a straight line. That's a dead giveaway that acceleration is constant.

There's nothing special about velocity going through zero. From the perspective of a frame of reference that's moving down at a constant velocity of 65 m/s toward the Earth, that ball is moving up throughout that 13 second interval (velocity is always positive). From the perspective of a frame of reference that's moving up at a constant velocity of 65 m/s away the Earth, that ball is moving down throughout that 13 second interval. While the velocities are different in those frames, the acceleration is the same across all three frames: 9.8 m/s2, downward.

Although "fall" in everyday English means "to move to a lower position under the effect of gravity", in Newtonian physics "free fall" means any motion of a body where its weight is the only force acting upon it, even if that motion in a particular time period in question involves moving to a higher position.

"Slowing down" or "speeding up" both describe a non-zero acceleration. Acceleration is the rate at which the velocity of an object changes over time. Suppose you measure velocities and accelerations as being positive if they are in the upward direction. Going from a speed of $9.8 m/s$ upwards to $0 m/s$ upwards over the course of a second is a change in speed of $0\ -\ 9.8 = -9.8 m/s$ over the course of that second, so the acceleration during that second was $-9.8 m/s^2$. Going from a speed of $0 m/s$ upwards to $-9.8 m/s$ during the following second is a change in speed of $-9.8\ -\ 0=-9.8 m/s$ over the course of that second, so the acceleration during that second is again $-9.8 m/s^2$.

The object in the video always remains along a straight vertical line, which is what they mean by "straight line motion".