Velocity and Position by Graphical Method

Velocity and displacement can be calculated from the area under the curve for the acceleration-time and velocity-time graphs, respectively.

For non-constant acceleration, the area under the acceleration-time curve is split into smaller rectangles of width, Δt, and height, average acceleration. Δt times average acceleration is the change in velocity.

The sum of areas of rectangles gives the total change in velocity during t₁ to t₂.

When Δt approaches zero, the average acceleration approaches instantaneous acceleration, and the sum can be replaced with an integral. The area is then represented as the integral of instantaneous acceleration.

Similarly, the area under the velocity-time curve is split into smaller rectangles of width, Δt, and height, average velocity. Delta t times average velocity is the change in position or the displacement. The total displacement during t₁ to t₂ is equal to the sum of the areas of all rectangles.

When Δt approaches zero, the average velocity approaches instantaneous velocity, the area is represented as the integral of instantaneous velocity from time t₁ to t₂.