what is the shape of a dislacement-time graph for an object that is constantly speeding up?

Answer 1

Well, it depends. If the acceleration is constant, then the velocity-time graph would be linear (a straight line at either an upward or downward angle). The displacement-time graph would be a portion of a parabola.

You can graph this if you have a graphing calculator or a graphing program on your computer. If acceleration is 1 foot per second per second, then its graph is y=1. The velocity-time graph would be y=x, and the displacement-time graph would be y=x^2 (x squared).

Of course, this is all assuming acceleration is constant. If acceleration changes, then the math behind it becomes calculus and the physics behind it becomes Rocket Science (literally!)