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.

5 Answers By Expert Tutors

By:

Walter B. answered • 10/05/15

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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

Gary C. answered • 10/05/15

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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

Christopher R.

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

Christopher R.

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.

tutor
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

Christopher R. 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

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