Question

A quick one, what will be the velocity-time graph of a projectile fired up with 20 m/s?
Also if you can explain me how to feel the nature of motion from these v-t graphs, some of them have driven me nuts lately.

Answer 1

That V=20 in the graph
since the derivative of velocity is acceleration, which is a constant here (ignoring air resistance)
Since the acceleration is equal to -g, that will be the slope of the velocity graph.
I let g=10 in the drawing and used the fact that the velocity at the top is zero to find the time at the top of the motion t'\[v-gt'=0\to t'=\frac vg=2\]the total time will be double that
The displacement will be given by the integral vdt, which is the area under the graph of v