Yes. I'm sure tiny-tim just mis-spoke. sjb-2812, a cute method I was taught, in high school, for finding tangents, and so derivatives, from a graph, used a small mirror. Hold the mirror on the graph at the point at which you want the tangent. Rotate the mirror about the vertical axis until the graph seems to go smoothly into its reflection in the mirror. Use the mirror as a straight edge to draw a line perpendicular to the curve. Now turn the mirror to draw a line perpendicular to that line and repeat the process to draw a line perpendicular to the original perpendicular and so tangent to the curve. From the values on the graph of the endpoints of that tangent line, you can find the slope of the tangent line and so the derivative of the function.
To find the acceleration, the second derivative of distance, you would need to do that in a number of different places to get a rough graph of "velocity versus time" and then repeat the process with that graph.
The simplest thing to do is to approximate the speed, at a number of points using the difference quotient of a number of near by points. Then, again, repeat the process to find the second derivative.
