The velocity is the integral of
acceleration
the acceleration function with respect to time.
The equation for velocity is given by:
v(t) = ∫ a(t) dt + C
where v(t) is the velocity function, a(t) is the acceleration function, t is the time variable, and C is the constant of integration.
Intuitively, this equation tells us that the velocity of an object at any given time is equal to the area under the acceleration curve from time zero to that time. The constant C represents the initial velocity of the object, which we need to know in order to fully determine the velocity function.
It’s important to note that the units of acceleration are meters per second squared (m/s²), while the units of velocity are meters per second (m/s). This means that when we integrate the acceleration function to find the velocity function, we are effectively “undoing” the effect of acceleration on the object’s velocity, as we are adding up the change in velocity over time due to acceleration.
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