I'm new to physics and trying to understand Newton's second law $F = ma$ but I don't think I'm grasping the concept of force very well. I've read other questions and answers on this law and it is my understanding, for now, that $F = ma$ is a "definition" of force based on the empirical "law" that the product $m \times a$ remains constant when the same amount of "force" (here the term used colloquially before formally defining it and assigning SI unit) is applied while varying the mass. But still, I don't seem to understand the full dynamics the law implies.
Suppose at time $t=0$, an external (?) force of $1$N is applied to a resting mass ($x'(0) = 0$) on a frictionless single-dimensional space with initial displacement $x(0) = 0$. The force applied is instantaneous in the sense that the bullet or whatever object that applied the force ricochets or disappears right away after contact with the resting mass. Here's my short train of thought that I needs guidance on:
- Since the force was instantaneous, $F(0) = 1$ and $F(t) = 0$ for $t > 0$. Then the second law will imply that the mass doesn't move at all since $p(t) = \int_0^t F(v) dv = 0$, meaning zero velocity.
- No no, that doesn't make sense. The initial condition $F(0) = 1$ applied to the resting mass will give instantaneous acceleration $a(0) = 1/m$. But how does acceleration or velocity evolve? It seems odd if acceleration is constant over time, but if it's not constant, then I don't see how to proceed to derive the trajectory.
I concluded I'm either misunderstanding what force is or I lack the kinematics toolbox or I am just completely loony and misguided overall. I'm just beginning to self-study basic physics and I feel like I'm starting off on the wrong foot. So here's me asking for some guidance. Please correct me and fill me in with what I am lacking/misunderstanding here.