Graphs of motion

The gradient of a displacement-time graph at a particular time gives the velocity of the object at that time.

Gradient = ${{change\;in\;displacement} \over {change\;in\;t}} = {{\Delta s} \over {\Delta t}}$ = velocity

The gradient of a velocity-time graph at a particular time gives the acceleration of the object at that time.

Gradient = ${{change\;in\;velocity} \over {change\;in\;t}} = {{\Delta v} \over {\Delta t}}$ = acceleration

The velocity-time and acceleration-time graphs for common motions are shown below. For the constant positive velocity graphs and the constant positive acceleration graphs the initial displacement is zero and the initial velocity is zero. For the constant negative acceleration graphs the initial displacement is negative and the initial velocity is positive.