Calculating acceleration from 2 tangent lines

[azn4lyf89]

I have a position vs. time graph which is slightly curved. I found the slope of 2 tangent lines which I know are the velocity. My question is how do I get the acceleration using these 2 slopes. One slope is 295cm/s and the other is 575cm/s. I know that avg acceleration is final velocity - initial velocity/ final time - initial time but because these points aren't at the initial and final times, I don't think I can use that.

 

[Clairefucious]

Then don't use final time in the acceleration equation! If acceleration is a constant, you can calculate it over any time interval.

 

[baba89]

To calculate the acceleration from these two tangent lines, you can use the formula for instantaneous acceleration, which is the derivative of velocity with respect to time. In other words, you can find the change in velocity (575cm/s - 295cm/s = 280cm/s) and divide it by the change in time between the two points on the graph. This will give you the instantaneous acceleration at that specific point on the graph.

However, if you want to find the average acceleration over a longer period of time, you can use the formula you mentioned: average acceleration = (final velocity - initial velocity) / (final time - initial time). In this case, you will need to choose two points on the graph that are closer to the initial and final times, and use the corresponding velocities and times to calculate the average acceleration.

It's important to note that the instantaneous acceleration at a specific point on the graph may be different from the average acceleration over a longer period of time, since the velocity and acceleration may be changing continuously. It may also be helpful to plot the data points and calculate the slope of the line connecting them to get a more accurate estimate of the acceleration.