Importance of Acceleration in Newtonian Physics I'm a just a hobby enthusiast in physics.
Why is acceleration important and what are the major things we would miss if we are unaware of this quantity in terms of Newtonian physics?
Like what would to you tell to a layman, how knowledge/discovery of acceleration have changed our world. Can't we just do everything with only velocity.
 A: The answer is that in the real world very few things move with a set velocity. To model aspects of the world- which is what physics and engineering are mainly about- you need to account for the fact that velocities are always changing. There are countless circumstances in which velocities are not constant- objects falling under gravity, circular motion, ballistics, kite flying, standing up and starting to walk, braking to avoid a pedestrian etc etc. In all these cases you need to take into account the changes in velocity, and that is all acceleration is.
A: As you know acceleration is the rate of change of velocity.
For a complete layman , who is not even concerned about Newton's laws, but just needs to describe some daily life events, one area where acceleration is helpful is in describing how fast an object would fall to the ground from a given height. Since, it is not falling at a constant velocity but at a constant acceleration of 9.8 m/sec^2 , he needs to understand the concept of  acceleration to describe this.
Note, this is even before learning about Newton's laws, it is just basic kinematics stuff to describe the motion of daily life things, which is needed to describe the motion of any objects which do not move at constant velocity like accelerating cars etc.
Once you learn the Newton's laws of motion, it becomes even more crucial to get a better understanding of the laws of nature
