Why is acceleration inversely proportional to the mass of an object, but directly proportional to force? Why is acceleration of an object inversely proportional to its mass, but directly proportional to force?
 A: A force is needed to change the speed of an object, and the change of speed is the acceleration. And mass can be thought of as a property of an object with which it resists acceleration (this is called inertia, https://en.wikipedia.org/wiki/Inertia for further reading). The relationship between these quantities is then $\vec F= m \cdot \vec a$.
A: By convention we decide that mass is an an important attribute of an object (since it measures the amount of "stuff" in the object), and then the equation
$\displaystyle a = \frac F m$
establishes that acceleration is proportional to applied force but inversely proportional to mass. This makes intuitive sense - the more "stuff" there is in an object, the more difficult it is to accelerate it.
But we could instead decide that the reciprocal of mass was the important attribute (in the same way as we sometimes talk about the electrical conductance of an object rather than its resistance). Let's call the reciprocal of mass "ssam", and denote it by "w". Then we would have
$a = F w$
In other words, acceleration is now directly proportional to both applied force and "ssam".
A: Force is rate of change of momentum:
$$ \vec F = \frac{d\vec p}{dt}$$
and $\vec p = m\vec v$. So:
$$ \vec F = m\frac{d\vec v}{dt} + \dot m \vec v$$
With $\dot m= 0$ and $\vec a\equiv d\vec v/dt$:
$$ \vec F=m\vec a $$
A: We know $F = m * a$ . Then , you rearrange the equation.
a = $\frac{ F }{m}$.
Case 1: Considering F to be const :
Acceleration is inversely proportional to mass.
Case 2: Considering m to be constant:
Acceleration is directly proportional to Force.
It will be a different question if you ask why is F = m *a. You can check this answer of mine if you do have.
https://physics.stackexchange.com/a/638836/287551
Hence proved. Do let me know if you have any difficulty.
