Newton's Second Law

Newton's second law says an object's acceleration depends on the net force acting on it and its mass. In the constant-mass situations used in most introductory physics problems, the relationship is:

F_{net} = ma

This means acceleration increases when the net force increases and decreases when the mass increases. The acceleration points in the same direction as the net force.

Use The Simulator To Test $F_{net} = ma$

Change force or mass one at a time and watch the acceleration update. With mass fixed, acceleration changes directly with force. With force fixed, acceleration changes inversely with mass.

Newton's second law simulator

Change the net force and mass to test Newton's second law in the constant-mass case. The motion prediction below assumes the net force stays constant during the chosen time interval, so the acceleration stays constant too.

Net force: 6 NNegative means left, positive means right.Mass: 2 kgAt the same net force, more mass means less acceleration.Initial velocity: 0 m/sThis only changes the motion prediction, not the acceleration.Observation time: 4 sUse this to see how constant acceleration changes velocity and position over time.

Your current calculation

Acceleration from net force and mass

a = F_net / m = 6 / 2 = 3 m/s^2

Velocity after 4 s

v = v_0 + a t = 0 + (3)(4) = 12 m/s

Displacement after 4 s

x = v_0 t + (1/2) a t^2 = 24 m

Direction check: net force is right, so acceleration is right.

If only force changes: with mass fixed, doubling the net force would change the acceleration to 6 m/s^2.

If only mass changes: doubling the mass would change the acceleration to 1.5 m/s^2.

What to notice in the motion

If the net force is zero, the acceleration is zero. That does not force the object to stop. It only means the velocity stays constant.

If the acceleration and velocity point the same way, the object speeds up. If they point in opposite directions, it slows down.

Here the object ends up 24 m to the right after 4 s, with a final velocity of 12 m/s.

Current motion trend: starting from rest or changing direction.

Force and motion view

Position after 4 s: 24 m to the right

Acceleration: 3 m/s^2 (right)

Acceleration vs. net force

For the current mass, this graph stays a straight line through the origin. That is the key pattern: if mass is fixed, acceleration changes in direct proportion to net force.

Current point: (6 N, 3 m/s^2)

When Newton's Second Law Becomes $F_{net} = ma$

The most general statement of Newton's second law is that net force equals the rate of change of momentum:

\vec{F}_{net} = \frac{d\vec{p}}{dt}

For a constant mass $m$ , momentum is $\vec{p} = m\vec{v}$ , so this reduces to

\vec{F}_{net} = m\vec{a}

That constant-mass form is the version most students first learn, and it is the version this widget models. If mass is changing, you should not assume $F_{net} = ma$ tells the whole story by itself.

Worked Example: 12 N On A 4 kg Cart

Suppose a cart has mass $4\ \mathrm{kg}$ and the net force on it is $12\ \mathrm{N}$ to the right. With constant mass,

a = \frac{F_{net}}{m} = \frac{12}{4} = 3\ \mathrm{m/s^2}

So the cart accelerates at $3\ \mathrm{m/s^2}$ to the right. If the same cart felt only $6\ \mathrm{N}$ , the acceleration would drop to $1.5\ \mathrm{m/s^2}$ . If the force stayed at $12\ \mathrm{N}$ but the mass increased to $8\ \mathrm{kg}$ , the acceleration would also be $1.5\ \mathrm{m/s^2}$ . That is the key idea: force pushes acceleration up, while mass resists that change.

What To Notice As You Move The Sliders

Do not just look for a bigger or smaller number. Look for the relationship itself.

Force changes acceleration directly.
Mass changes acceleration inversely.
Zero net force means zero acceleration, even if the object is already moving.

That last point matters. Newton's second law connects force to acceleration, not force to velocity.

Try A Similar Force-And-Mass Case

Try your own version with one variable fixed. First double the force while keeping mass constant. Then reset and double the mass while keeping force constant. If you can predict the new acceleration before checking the widget, you are using the law instead of memorizing it.

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