Physics · MOTION IN A STRAIGHT LINE

The instantaneous acceleration of an object is defined as the limiting value of average acceleration as the time interval \( \Delta t \) approaches zero. Mathematically, it is expressed as:

1. \( a = \frac{dx}{dt} \)
2. \( a = \frac{d^2x}{dt^2} + v \)
3. \( a = \frac{dv}{dx} \)
4. \( a = \lim_{\Delta t \to 0} \frac{\Delta v}{\Delta t} = \frac{dv}{dt} \)