The rate of change of velocity with respect to time is known as acceleration. It represents how quickly an object's velocity is changing over time. Mathematically, acceleration (a) is defined as the derivative of velocity (v) with respect to time (t) or the second derivative of position (s) with respect to time:
a = dv/dt = d²s/dt²
In other words, acceleration is the rate at which velocity is changing. If an object's velocity is increasing, the acceleration is positive, while if the velocity is decreasing, the acceleration is negative (often referred to as deceleration). If the velocity remains constant, the acceleration is zero.
Acceleration is typically measured in units of distance per time squared, such as meters per second squared (m/s²) in the International System of Units (SI). It represents how much an object's velocity changes over a specific time interval.
It's important to note that acceleration is a vector quantity, meaning it has both magnitude (the numerical value) and direction. Thus, it is possible for an object to accelerate even if its speed remains constant, as long as there is a change in direction.