# Change in scales causing change in gradient?

Richie Smash
Hello I plotted a graph of velocity against time only to realise that I needed more space on the X axis, so I changed my scale from instead of 2cm= 10 seconds to 2cm =20 seconds.

My Y axis remained constant with a scale of 2cm= 10 m/s

However, the gradient I got from the first scale was 1.15m/s2 and this even coincides with the data given.

But with my new readjusted scale to fit the page I'm getting a gradient of 2.4 m/s2.

How can this be? the graph is a straight line so the acceleration is constant according to the data given, am I plotting this wrong??

## Answers and Replies

Mentor
However, the gradient I got from the first scale was 1.15m/s2 and this even coincides with the data given.
How are you calculating that gradient?

Richie Smash
Dr Claude, I am using the triangle method and then dividing the vertical units by the horizontal units, using two poitns that are NOT given in the data but instead two points from the line of best fit I drew, which is standard practice for this level

Mentor
It's somewhat hard to determine what you did wrong without seeing any work or a picture of your chart.

If you've computed the slope using algebraic means you should get the same value ie ##(y1-y0)/(x1-x0)## for your acceleration (velocity/seconds ie ##m/s^2##)

If instead you are using the grids on your graph paper then of course you'll get something different unless you adjust for the x length of the grid element.

As an example, if you computed it using ##(y1-y0)## in centimeters over ##(x1-x0)## in centimeters then that is wrong.

Whereas if you computed it ##( (y1-y0).in.cm) * (10m/s.per.cm) )## over ##( ((x1-x0).in.cm) * (20 seconds.per.cm))##

• scottdave
Mentor
Dr Claude, I am using the triangle method and then dividing the vertical units by the horizontal units
Then my guess is that you are not calculating the units correctly.

Can you post the plots you did? It may help in figuring where you are going wrong.

Richie Smash
Ok here are my images with the scales represented above and the data presented to plot orginally...

However I realized what I did wrong... I simply forgot to convert thehorizontal units in my new graph the second picture, to suit...it was just one tiny mistake.... how DO I avoid these? The test I'm studying for specifically wants me to do the triangle method, bigger than half the line, etc.

BUt theres not much time and I somtimes I just make silly errors, now I feel dumb sorry for this silly post

#### Attachments

Mentor
This is NOT a silly post. We all learn from our mistakes.

The most humbling thing is that we learn we make mistakes. The second thing is in reconstructing our reasoning we might determine why we made the mistake.

To be fair, you caught your mistake and that is a very hopeful sign that you're really grasping the subject. This mistake will stick with you forever and I'm sure you won't make this same mistake twice. (fingers crossed). You can even pass it on to your kids with some sagely advice.

Our mistakes teach us so much and eventually we get to teach them to others.

• DrClaude and Richie Smash
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