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Velocity Versus Time Graph Calculator Online

The Velocity Versus Time Graph Calculator is a valuable tool that helps users visualize and calculate different aspects of motion from velocity-time data. It is particularly useful in educational contexts, aiding in the study of kinematics, the analysis of motion without considering its causes.

Formula of Velocity Versus Time Graph Calculator

The calculator uses various formulas to interpret data from velocity vs. time graphs:

Area Under the Curve (Displacement)

Displacement (s) is calculated by the area under the velocity vs. time graph. For graphs with straight-line segments, use:

s = integral of v(t) dt

For discrete time intervals, use:

s = sum of (vi * Δti)

where vi is the velocity at each interval, and Δti is the duration of each interval.

Slope of the Curve (Acceleration)

Acceleration (a) is the slope of the velocity vs. time graph. For linear segments, use:

a = Δv / Δt

where Δv is the change in velocity and Δt is the change in time.

Velocity at a Specific Time

To find velocity (v) at a specific time (t), use:

v(t) = v0 + a * t

where v0 is the initial velocity and a is constant acceleration.

Average Velocity

Average velocity (v̄) over a time period is calculated as:

v̄ = s / t

where s is the total displacement and t is the total time.

Instantaneous Velocity

The instantaneous velocity at any time (t) is:

v = ds / dt

where ds is the small change in displacement and dt is the small change in time.

Utility Table

Below is a table with common terms used in velocity calculations, along with their definitions and applications:

Example of Velocity Versus Time Graph Calculator

Consider a scenario where a car accelerates uniformly from a stop. Using the Velocity Versus Time Graph Calculator, we demonstrate how to calculate the car’s displacement after 5 seconds, assuming an acceleration of 2 m/s².