Question

Why is that an angle determines the sign of average acceleration on a distance versus time graph?

Answer 1

Displacement versus time graph give us velocity, and from graph we can find out that the velocity is increasing or decreasing with time.

If the velocity is increasing with time then acceleration is positive, and if it is decreasing with time then acceleration is negative. So, slope (or angle) can tell us about the sigh of average acceleration on a displacement time graph.