# How to convert a slope to an acceleration?

• Ellio
In summary, the conversation revolved around a physics experiment involving releasing a tape from a certain height and marking its position at different times. The student was struggling with one of the exercises involving calculating the slope and acceleration from a graph. The expert explained that in the first graph, the slope represents the change in position over time, while in the second graph, the slope represents the change in position over the square of time. They also clarified that for an object with constant acceleration, the slope of the second graph is equal to half of the acceleration. This helped the student better understand the concept.
Ellio
Homework Statement
"From the slope (of the graphic) you calculated, determine the acceleration of the object."
Relevant Equations
Slope: Δy/Δx
Gravitational acceleration on Earth ≅ 9.81 m/s²
Hello, I hope you are all very well.
I am in second year of High School and I have a practical work in physics.
The experiment was to release a long tape with a mass of 40g at the end from a certain height. An instrument would hit the tape 50 times/s and put a mark each time. From that we have to complete a series of exercises.

One of the exercise is however causing me some trouble. We had to write down the different position of all the mark that are on the tape on a graphic. The first one is a x(t) graphic and the second one x(t²).
I got a curved line with the first one:

and a straight line with the x(t²) graphic:

Here's my problem... We're told to first calculate the slope of this (x(t²))graphic. The expression to calculate a slope being Δy/Δx. The very last "position" (y axis) on the graphic is 0.610m at 0.1296s² (x axis).
0.610/0.1296 ≃ 4.708
Assuming that the slope = 4.708, how could I know find the acceleration from that ? The graphic being a constant straight line, isn't the acceleration = 0 ?
But that's not the case (a=9.81), if I'm not mistaken...

I am really sorry to bother you with a such a stupid question ! I really thank you in advance.

(ps.: I'm Swiss, sorry for my English...)

In the first graph, you plot x vs t, and you see the slope, which is Δx/Δt increasing. In the second graph, you plot x vs t^2, so the slope is Δx/Δ(t^2). Since an object moving with constant acceleration a follows the equation $x = \frac{1}{2} a t^2$, the slope of this line (Δx/Δ(t^2))is 1/2 a. This is just what you found. Does this help?

phyzguy said:
In the first graph, you plot x vs t, and you see the slope, which is Δx/Δt increasing. In the second graph, you plot x vs t^2, so the slope is Δx/Δ(t^2). Since an object moving with constant acceleration a follows the equation $x = \frac{1}{2} a t^2$, the slope of this line (Δx/Δ(t^2))is 1/2 a. This is just what you found. Does this help?
Absolutely, it really helped me thank you a lot !

## What is the formula for converting a slope to an acceleration?

The formula for converting a slope to an acceleration is a = m/s², where a is the acceleration in meters per second squared and m is the slope in meters per second.

## How do I determine the slope from a given acceleration?

To determine the slope from a given acceleration, you can use the formula m = a * s, where m is the slope in meters per second and s is the time in seconds.

## Can the slope and acceleration be negative values?

Yes, both the slope and acceleration can be negative values. A negative slope indicates a downhill or decreasing motion, while a negative acceleration indicates a decrease in velocity over time.

## What is the difference between slope and acceleration?

Slope is a measure of the steepness or incline of a line, while acceleration is a measure of the change in velocity over time. Slope is a constant value, while acceleration can vary depending on the rate of change.

## Can I convert a slope to acceleration without knowing the time interval?

No, you need to know the time interval in order to convert a slope to acceleration. The formula for acceleration includes time as a variable, so without knowing the time interval, you cannot accurately determine the acceleration.

• Introductory Physics Homework Help
Replies
15
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
13
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
4K
• Introductory Physics Homework Help
Replies
11
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
22
Views
3K
• Introductory Physics Homework Help
Replies
13
Views
2K
• General Math
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
48
Views
8K