If you integrate velocity, you obtain displacement or position. Integration is the mathematical operation that reverses the process of differentiation. Differentiation is used to calculate velocity by taking the derivative of the position with respect to time, while integration does the opposite.
To clarify further, let's consider the basic equations:
Velocity: Velocity is the rate of change of displacement with respect to time. Mathematically, it can be expressed as: v(t) = d(x(t))/dt where v(t) represents the velocity at time t, x(t) is the position at time t, and d/dt denotes the derivative with respect to time.
Displacement/Position: Displacement or position is the integral of velocity with respect to time. Mathematically, it can be expressed as: x(t) = ∫v(t) dt where x(t) represents the displacement or position at time t, and the integral symbol (∫) denotes the integration operation.
Integrating velocity over a specific time interval gives you the change in position during that interval. It provides information about how the position of an object changes over time.
It's important to note that integration introduces a constant of integration, which represents the initial position at a specific reference point. To determine the exact position, additional information or boundary conditions are required, such as the initial position or velocity at a specific time.