An example of 2D collisions using JavaScript Canvas

Object collisions with canvas

class State {
  constructor(display, actors) {
    this.display = display;
    this.actors = actors;
  }

  update(time) {

    /**
     * provide an update ID to let actors update other actors only once
     * used with collision detection
     */
    const updateId = Math.floor(Math.random() * 1000000);
    const actors = this.actors.map(actor => {
      return actor.update(this, time, updateId);
    });
    return new State(this.display, actors);
  }
}


class Vector {
  constructor(x, y) {
    this.x = x;
    this.y = y;
  }

  add(vector) {
    return new Vector(this.x + vector.x, this.y + vector.y);
  }

  subtract(vector) {
    return new Vector(this.x - vector.x, this.y - vector.y);
  }

  multiply(scalar) {
    return new Vector(this.x * scalar, this.y * scalar);
  }

  dotProduct(vector) {
    return this.x * vector.x + this.y * vector.y;
  }

  get magnitude() {
    return Math.sqrt(this.x ** 2 + this.y ** 2);
  }

  get direction() {
    return Math.atan2(this.x, this.y);
  }
}

class Canvas {
  constructor(parent = document.body, width = 400, height = 400) {
    this.canvas = document.createElement('canvas');
    this.canvas.width = width;
    this.canvas.height = height;
    parent.appendChild(this.canvas);
    this.ctx = this.canvas.getContext('2d');
  }

  sync(state) {
    this.clearDisplay();
    this.drawActors(state.actors);
  }

  clearDisplay() {

    // opacity controls the trail effect set to 1 to remove
    this.ctx.fillStyle = 'rgba(255, 255, 255, .4)';
    this.ctx.fillRect(0, 0, this.canvas.width, this.canvas.height);
    this.ctx.strokeStyle = 'black';
    this.ctx.strokeRect(0, 0, this.canvas.width, this.canvas.height);
  }

  drawActors(actors) {
    for (let actor of actors) {
      if (actor.type === 'circle') {
        this.drawCircle(actor);
      }
    }
  }

  drawCircle(actor) {
    this.ctx.beginPath();
    this.ctx.arc(actor.position.x, actor.position.y, actor.radius, 0, Math.PI * 2);
    this.ctx.closePath();
    this.ctx.fillStyle = actor.color;
    this.ctx.fill();
  }
}

class Ball {
  constructor(config) {
    Object.assign(this,
      {
        id: Math.floor(Math.random() * 1000000),
        type: 'circle',
        position: new Vector(100, 100),
        velocity: new Vector(5, 3),
        radius: 25,
        color: 'blue',
        collisions: [],
      },
      config
    );
  }

  update(state, time, updateId) {

    /**
     * if slice occurs on too many elements, it starts to lag
     * collisions is an array to allow multiple collisions at once
     */
    if (this.collisions.length > 10) {
      this.collisions = this.collisions.slice(this.collisions.length - 3);
    }

    /**
     * this is the most stable solution to avoid overlap
     * but it is slightly inaccurate
     */
    for (let actor of state.actors) {
      if (this === actor || this.collisions.includes(actor.id + updateId)) {
        continue;
      }

      /**
       * check if actors collide in the next frame and update now if they do
       * innaccurate, but it is the easiest solution to the sticky collision bug
       */
      const distance = this.position.add(this.velocity).subtract(actor.position.add(actor.velocity)).magnitude;

      if (distance <= this.radius + actor.radius) {
        const v1 = collisionVector(this, actor);
        const v2 = collisionVector(actor, this);
        this.velocity = v1;
        actor.velocity = v2;
        this.collisions.push(actor.id + updateId);
        actor.collisions.push(this.id + updateId);
      }
    }
    
    // setting bounds on the canvas prevents balls from overlapping on update
    const upperLimit = new Vector(state.display.canvas.width - this.radius, state.display.canvas.height - this.radius);
    const lowerLimit = new Vector(0 + this.radius, 0 + this.radius);

    // check if hitting left or right of container
    if (this.position.x >= upperLimit.x || this.position.x <= lowerLimit.x) {
      this.velocity = new Vector(-this.velocity.x, this.velocity.y);
    }

    // check if hitting top or bottom of container
    if (this.position.y >= upperLimit.y || this.position.y <= lowerLimit.y) {
      this.velocity = new Vector(this.velocity.x, -this.velocity.y);
    }

    const newX = Math.max(Math.min(this.position.x + this.velocity.x, upperLimit.x), lowerLimit.x);
    const newY = Math.max(Math.min(this.position.y + this.velocity.y, upperLimit.y), lowerLimit.y);

    return new Ball({
      ...this,
      position: new Vector(newX, newY),
    });
  }

  get area() {
    return Math.PI * this.radius ** 2;
  }

  get sphereArea() {
    return 4 * Math.PI * this.radius ** 2;
  }
}

// see elastic collision: https://en.wikipedia.org/wiki/Elastic_collision
const collisionVector = (particle1, particle2) => {
  return particle1.velocity
    .subtract(particle1.position
      .subtract(particle2.position)
      .multiply(particle1.velocity
        .subtract(particle2.velocity)
        .dotProduct(particle1.position.subtract(particle2.position))
        / particle1.position.subtract(particle2.position).magnitude ** 2
      )

      // add mass to the system
      .multiply((2 * particle2.sphereArea) / (particle1.sphereArea + particle2.sphereArea))
    );
};

const isMovingTowards = (particle1, particle2) => {
  return particle2.position.subtract(particle1.position).dotProduct(particle1.velocity) > 0;
};

const runAnimation = animation => {
  let lastTime = null;
  const frame = time => {
    if (lastTime !== null) {
      const timeStep = Math.min(100, time - lastTime) / 1000;

      // return false from animation to stop
      if (animation(timeStep) === false) {
        return;
      }
    }
    lastTime = time;
    requestAnimationFrame(frame);
  };
  requestAnimationFrame(frame);
};

const random = (max = 9, min = 0) => {
  return Math.floor(Math.random() * (max - min + 1) + min);
};

const colors = ['red', 'green', 'blue', 'purple', 'orange'];

const collidingBalls = ({ width = 400, height = 400, parent = document.body, count = 50 } = {}) => {
  const display = new Canvas(parent, width, height);
  const balls = [];
  for (let i = 0; i < count; i++) {
    balls.push(new Ball({
      radius: random(8, 3) + Math.random(),
      color: colors[random(colors.length - 1)],
      position: new Vector(random(width - 10, 10), random(height - 10, 10)),
      velocity: new Vector(random(3, -3), random(3, -3)),
    }));
  }
  let state = new State(display, balls);
  runAnimation(time => {
    state = state.update(time);
    display.sync(state);
  });
};

collidingBalls();

@StarTraX and @joshuabradley012, it seems that whenever the mass multiplier evaluates to anything greater than 1, it adds entropy and speed into the system. So, putting the multiplier under 1 reduces both the randomness and acceleration.