Kinematics - Theory & Concepts - Kinematics Graph

Study the geometry of motion including displacement, velocity, acceleration, free fall, projectile motion, and relative velocity.

Open the complete lesson

Interactive engineering simulation

Kinematics Motion & Graph Simulator

Adjust initial velocity and acceleration, and scrub time. Analyze how position, velocity, and acceleration curves behave, and observe that the area under the v-t curve equals displacement.

Select Active Graph

Initial Velocity (v0)6.0 m/s

m/s

-10.0–20.0

Drag for exploration or enter an exact value. Press Enter to apply; Escape restores the current value.

Constant Acceleration (a)1.5 m/s²

m/s²

-5.0–5.0

Drag for exploration or enter an exact value. Press Enter to apply; Escape restores the current value.

Duration8.0 s

2.0–16.0

Drag for exploration or enter an exact value. Press Enter to apply; Escape restores the current value.

Time Scrubber4.0 s

0.0–8.0

Drag for exploration or enter an exact value. Press Enter to apply; Escape restores the current value.

Governing Formulas

Position & Velocity

x(t) = v_0 t + \frac{1}{2}a t^2, \quad v(t) = v_0 + a t

Calculus Theorem

v(t) = \frac{dx}{dt}, \quad x(t) = \int_{0}^{t} v(\tau) d\tau \quad (\text{Area})

Position (x)

36.00 m

Velocity (v)

12.00 m/s

Acceleration

1.50 m/s²

Model scope and verification

Use the displayed units and idealizations, then verify the governing balance or compatibility equation before interpreting the result.

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