Summary - Acceleration

Galileo showed that when air resistance is negligible all falling bodies have the same motion regardless of mass. Moreover, their v-t graphs are straight lines. We therefore define a quantity called acceleration as the slope, Δv/Δt, of an object's v-t graph. In cases other than free fall, the v-t graph may be curved, in which case the definition is generalized as the slope of a tangent line on the v - t graph. The acceleration of objects in free fall varies slightly across the surface of the earth, and greatly on other planets.

Positive and negative signs of acceleration are defined according to whether the v - t graph slopes up or down. This definition has the advantage that a force in a given direction always produces the same sign of acceleration.

The area under the v - t graph gives Δx, and analogously the area under the a - t graph gives Δv.

For motion with constant acceleration, the following three equations hold:

They are not valid if the acceleration is changing.