Question

can the equation,a=vf-vi/tf-ti be used in a situation where the acceleration varies with time? Can they be used when the acceleration is zero?

Answer 1

Average acceleration is defined as ratio of change in velocity and time

$a_{avg}=\frac{\text{change in velocity }}{\text{time elapsed}}=\frac{v_f-v_i}{t_f-t_i}$

Thus the above formula gives average acceleration.

Instantaneous acceleration is limit of average acceleration as time interval goes to zero.

$a_{inst}=\lim_{t_f-t_i\to0}a_{avg}=\lim_{t_f-t_i\to 0}\frac{v_f-v_i}{t_f-t_i}=\frac{dv}{dt}$

Instantaneous acceleration is a function of time and it may vary from one instant to another.

Average acceleration is valid for the complete time interval.

Hence the above formula cannot be used to find the acceleration which is varying with time.

But the above formula can be used when acceleration is zero (since it is constant, average acceleration and instantaneous acceleration are same )