# F=ma

Does Newton’s Second Law only apply for particles with constant acceleration?

Also, I’m struggling to understand constant acceleration vs non-constant acceleration. How do we represent and imply non-constant acceleration, since (I think) the acceleration is changing with time.
Original post by NaBrO
Does Newton’s Second Law only apply for particles with constant acceleration?

Also, I’m struggling to understand constant acceleration vs non-constant acceleration. How do we represent and imply non-constant acceleration, since (I think) the acceleration is changing with time.

Newton's Second Law acts on particles when they are accelerated, apart from constant or non-constant. A force generally works when an object is in acceleration.

Acceleration is constant when the velocity is constant too. Whenever velocity has no consistent change according to the changing time, the acceleration can't betoo. Acceleration and velocity are connected.
(edited 2 years ago)
Original post by NaBrO
Does Newton’s Second Law only apply for particles with constant acceleration?

Also, I’m struggling to understand constant acceleration vs non-constant acceleration. How do we represent and imply non-constant acceleration, since (I think) the acceleration is changing with time.

No.
f = ma
applies when the force f varies, constant, zero, ...

When a constant force is applied to a particle, this produces a constant acceleration f/m. Then all the usual suvat equations apply. So vertical motion with only a (constant) gravitational force would produce a constant acceleration scenario.

When the force varies (with time), you have to use calculus (integration) to solve for the velocity and position as
acceleration = dv/dt = d^2 x/dt^2
So integrate f/m once to get the velocity, v, and twice to get the displacement x, This reduces to suvat equations when f is constant. If you also included a velocity (time) dependent drag into the previous vertical motion scenario, then acceleration would not be constant and you'd have to use calculus to solve the problem.

When f is zero, Newton 1 (inertia) applies and the current motion is unchanged. This is Newton 2 with f=a=0.
(edited 2 years ago)
F=ma
Even if a=0 you can still use the formula.

Acceleration is how much the velocity of an object changes every second.
For instance, an acceleration of 3 m.s-2 means that every 1 second, the velocity of the object increases by 3 m.s-2; in other words, the object is speeding up.

Accelation = 0 if the velocity of the object is not changing, ie, a stationary object and an object moving at a constant speed have no acceleration.

Uniform acceleration means that the velocity increases by equal amounts every 1 second. Although acceleration is constant, velocity is increasing.
The same can be said for negative acceleration, when velocity is decreasing