Cynthia M.

asked • 10/05/15

As a ball falls, its acceleration is what?

As a ball falls, its acceleration is...
 
Multiple Choice:
A) positive
B) negative
C) it has no acceleration
 
I know the answer is A) positive. But why? Please explain.

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Inactive Tutor answered • 10/05/15

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Hi Cynthia,
 
The reason that we say that the acceleration is positive is that the velocity of the ball (given by velocity = acceleration x time) will increase as the ball falls. If the acceleration were negative, then the ball ball would slow down like when you brake a car.
 
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Hilton T.

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The ball can still speed up if both the acceleration and the velocity were negative.

Consider a ball that is thrown upward at 40 m/s. Assume that the acceleration due to gravity changes the velocity by 10 m/s every second. Then the velocity at very second is as follows:

t         0           1           2           3            4           5            6            7            8

v        40         30        20        10          0           -10       -20        -30        -40
 
a       -10        -10     -10       -10        -10        -10       -10        -10         -10                 

A plot of v versus t produces a straight line graph of negative slope (-10 m/s/s). Notice that for the first 4 seconds, the ball is slowing down until it reaches maximum height. For the next four seconds it is speeding up as it is falling, even though both velocity and acceleration are negative.
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10/12/15

Inactive Tutor answered • 10/05/15

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The acceleration is positive because as the ball drops the speed increases. If speed increases, then acceleration is positive. If speed decreases, then acceleration is negative. If the speed stays constant, then there is no acceleration. 
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Hilton T.

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It is incorrect to say that if the speed stays constant, then there is no acceleration. Consider a car going around on a curves road. at a constant 10 m/s. The speed is constant; the velocity is not since the direction is changing by the second. Since there is a change in velocity, then there is an acceleration - known as centripetal acceleration. It is correct to say that if the velocity (not speed) is constant, then there is no acceleration.
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10/11/15

Inactive Tutor

Hilton, this is incorrect. Acceleration is defined as the change in velocity over time. If there is no change in velocity there is no acceleration. In the example you have given here, you introduced a changing velocity and therefore an acceleration. And it is irrelevant to the question asked and to the straight forward answer that Gary had given.
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10/18/15

Hilton T.

tutor
Christopher,
You are not reading the last line of Gary's comment correctly. Now, which is correct? If the speed stays constant, then there is no acceleration, or if the velocity stays constant, then there is no acceleration. You are talking about velocity; Gary is talking about speed. Are speed and velocity the same? I used an example just to illustrate this point.
 
 
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10/18/15

Inactive Tutor

I did not read it incorrectly at all. We generally refer to speed as |v| so we remove the vector component which would be used to define a negative or positive direction. Simplistically,|Δv|/t is still the acceleration in terms of speed. And if there is no change in speed there is no acceleration. The error in Gary's comments was actually assuming you'd have negative speed and that acceleration in terms of speed where you have no vector would ever be negative.
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10/18/15

Hilton T.

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This is my final comment on this topic. However, I pose this question to you. If the acceleration of the ball as it is rising is considered as positive, and when it is falling  negative, then what is the acceleration of the ball when it is at its maximum height? Is it positive, Is it negative, or is it zero? If it is not zero, then what is its magnitude and direction?
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10/18/15

Hilton T.

tutor
Sorry, I meant to change the negative and positive as follow. If the acceleration of the ball as it is rising is considered as negative, and when it is falling positive, then what is the acceleration of the ball when it is at its maximum height? Is it positive, Is it negative, or is it zero? If it is not zero, then what is its magnitude and direction?
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10/19/15

Hilton T. answered • 10/11/15

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 Negative.
 
The acceleration of the ball is negative by widely acceptable convention. If we treat direction up as positive, and direction down as negative, then a falling ball will have both negative velocity and negative acceleration. A ball that is projected upward will have positive velocity, and negative acceleration.
Start getting accustomed to using direction up as positive and direction down as negative. Colleges, high schools, and text books use this convention.
 
You need a book that have problems of this nature and strategies that can be used to solve them. I recommend "Score High in Physics" which is available on the Amazon website. It is a low cost ebook that can be readily downloaded to ipad, kindle, computer, etc.
 
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Inactive Tutor answered • 10/05/15

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Hilton T.

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The slope is negative, so the acceleration is negative.
Consider a ball that is thrown upward at 40 m/s. Assume that the acceleration due to gravity changes the velocity by 10 m/s every second. Then the velocity at very second is as follows:
 
t    0       1        2         3         4          5          6         7         8
 
v   40     30     20      10        0         -10       -20    -30      -40
 
A plot of v versus t produces a straight line graph of negative slope (-10 m/s/s). Notice that for the first 4 seconds, the ball is slowing down until it reaches maximum height. For the next four seconds it is speeding up as it is falling.
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10/11/15

Hilton T.

tutor
The hyperphysics link for the velocity time graph does not apply to an object that is falling under gravity.
 Consider the following situation.

A ball that is thrown upward at 40 m/s. Assume that the acceleration due to gravity changes the velocity by 10 m/s every second. Then the velocity at every second is as follows:

t   0     1     2    3    4    5       6    7       8

v 40   30   20 10   0  -10  -20  -30  -40

A plot of v versus t produces a straight line graph of negative slope (-10 m/s/s). Notice that for the first 4 seconds, the ball is slowing down until it reaches maximum height. For the next four seconds it is speeding up as it is falling.
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10/11/15

Inactive Tutor answered • 10/05/15

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By convention, the initial direction of motion decides the signs of all the physical quantities of motion like displacement, velocity and acceleration. If the initial direction of motion is upward, all the upward quantities will be positive than all the opposite will be negative. And in this particular case, the initial direction of motion is downward hence all downward pointing quantities will be positive. In general, if your initial velocity is reducing, then it is retardation hence negative acceleration as in case of upward motion. If the object is dropped, so the initial direction of motion is downward which increases the velocity and hence acceleration is positive.
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