Difference between ForceMode.Force/Acceleration/Impulse/VelocityChange?

Let's talk a little about physics.

Equations: Force = mass * acceleration, F = ma Impulse = change in momentum, J = (delta) mv Force = Impulse/time. = F = J/t

First, understand that adding an instant force or acceleration is mathematically impossible, so Unity applies the force/acceleration gradually over a time period for ForceMode.Force and ForceMode.Acceleration. This time period is normally 1 second. (meaning it technically adds an impulse... but enough of that)

Secondly, adding an instant impulse is mathematically possible because an impulse is a force applied over a time period. Same with ForceMode.VelocityChange.

Key: m = rigidbody mass Q = Vector3 number parameter t = Force application duration, normally 1 second in Unity

ForceMode.Force adds the exact force on the object on that Frame. Therefore, the rigidbody the force is exerted on will accelerate at an acceleration of Q/m for t seconds. If you know your integrals... acceleration is the first derivative of velocity and so the velocity of the object will gradually change by (Q/m)*t = Q/m for 1 second.

ForceMode.Impulse adds an instant impulse on the object on that frame. An impulse changes the momentum of the object, and because the mass stays the same, the velocity of the object instantly changes by Q/m.

ForceMode.Acceleration directly adds an acceleration to the object, regardless of its mass. So the change in velocity of the object becomes Qt = Q for 1 second. Equivalent to applying a ForceMode.Force of m*Q.

ForceMode.Velocity instantly changes the velocity of the object by Q, regardless of its mass. Equivalent of applying an Impulse of m*Q.

Summary: the main difference is whether the amount is applied instantly or not. Impulse and VelocityChange are instant (therefore not realistic in real life), ForceMode.Force and ForceMode.Acceleration are gradual along 1 second (but are misleading in name).

My final answer

ForceMode.Force = Time.fixedDeltaTime * ForceMode.Impulse

ForceMode.Acceleration = Time.fixedDeltaTime * ForceMode.VelocityChange

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ForceMode.Force = mass * velocityChange / timeChange

ForceMode.Impulse = mass * velocityChange / timeChange / Time.fixedDeltaTime

I created a cuboid in Unity and added rigidbody to the cuboid. Disabled gravity. Wrote a movable scrpit in Start() method to test the differences between these 4 forcemodes. Below is my test results and summary.

Equations

• ForceMode.VelocityChange = Number of Force

• ForceMode.Acceleration = Number of Force / PhysicsFramerate

• ForceMode.Impulse = Number of Force / Mass

• ForceMode.Force = Number of Force / Mass / PhysicsFramerate

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Example

[ForceMultiplier= 200]

[Mass = 2 ]

[PhysicsFramerate = 50]

• ForceMode.VelocityChange = 200= 200
  

• ForceMode.Acceleration = 200 / 50 = 4
  

• ForceMode.Impulse = 200 / 2 = 100
  

• ForceMode.Force = 200 / 2 / 50 = 2

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Explanation

• Any force was effective in 1 second only. So if you call the force in the Start() method, it only applies 1 second. But it will apply every second in the Update()/FixedUpdate() method.

• Unity locked the PhysicsFramerate to 50 frames per second (This is different from your application's framerate), which does not change.

• If no other force applied(e.g. gravity), the speed will remain the same after the force applied.

• Time.deltaTime represents the actual frame time, which can be used to make the acceleration smoother.