According to the actual definitions in physics, instantaneous velocity and acceleration can be observed and measured. However, it's important to understand the context and limitations of these observations.
In physics, velocity is defined as the rate of change of displacement with respect to time. Instantaneous velocity refers to the velocity of an object at a particular instant in time. It is determined by calculating the derivative of the object's position function with respect to time.
While it is not possible to directly observe or measure instantaneous velocity in real-time, it can be approximated by measuring an object's position over very short time intervals and calculating the average velocity over that interval. By reducing the time interval, the approximation becomes more accurate and closer to the true instantaneous velocity.
Similarly, acceleration is defined as the rate of change of velocity with respect to time. Instantaneous acceleration refers to the acceleration of an object at a particular instant in time. It can be determined by calculating the derivative of the object's velocity function with respect to time.
Just like with instantaneous velocity, it is not possible to directly observe or measure instantaneous acceleration in real-time. However, by measuring an object's velocity over very short time intervals and calculating the average acceleration over that interval, we can approximate the instantaneous acceleration. Again, reducing the time interval improves the accuracy of the approximation.
It's worth noting that while instantaneous velocity and acceleration can be conceptually understood and mathematically defined, their direct observation is limited by practical constraints. In experiments and real-world situations, we often rely on measuring and analyzing motion over finite time intervals to estimate these quantities accurately.