instantaneous acceleration
derivative of velocity v'(t) s(t)
Instantaneous acceleration is the rate at which the velocity of an object changes at a specific moment in time. It is the change in velocity divided by the change in time, where the change in time is infinitesimally small (approaching zero) and the instantaneous acceleration is the value of this expression at that moment in time. Mathematically, the instantaneous acceleration can be represented as:
a = lim (∆v/∆t), as ∆t → 0
Where a is the instantaneous acceleration, and ∆v and ∆t represent the change in velocity and change in time, respectively.
For example, if a car is travelling at a constant speed of 60 km/h, its instantaneous acceleration is zero because there is no change in velocity. However, if the car suddenly accelerates to 80 km/h in five seconds, its instantaneous acceleration at the five-second mark can be calculated as:
a = (80 km/h – 60 km/h) / 5 s = 4 m/s²
This means that the car is accelerating at a rate of 4 m/s² at that specific moment in time.
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