Javascript assignment multiplication operators in a loop as a Math function

Mircea Published at Dev

Mircea

I am doing the following calculations in a loop:

var i = 0;
var times = 200;
var friction = 0.9925;
var velocity = 10;
var position = 100;

for (; i < times; i += 1) {
    velocity *= friction;
    position += velocity;
}

console.log(velocity) // 2.218723008169958 
console.log(position) // 1129.722321918849

I would like to rewrite that as a Math function and eliminate the loop if possible.

Looking trough the JavaScript Math object: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math I am not seeing something to handle this.

Is there a better way of getting to the final result using a Math formula?

Hauke P.

Solve it with math:

// v_1 = v_0 * f
// p_1 = p_0 + v_1
// 
// p_2 = p_1 + v_1 * f
//     = p_0 + v_1 + v_1 * f
//     = p_0 + v_0 * f + v_0 * f * f
//     = p_0 + v_0 * (f + f^2)

At this point you might see that p_n = p_0 + v_0 * (f + f^2 + f^3 + ... + f^n).

From your formulary you might know that this is true:

Formula

Therefore p_n = p_0 + v_0 * f * (1 - f^n) / (1 - f).

Transferred to JavaScript you get this:

var n = 200;
var friction = 0.9925;
var velocity_0 = 10.0;
var position_0 = 100.0;

var velocity_n = velocity_0 * Math.pow(friction, n);
var position_n = position_0 + velocity_0 * friction * (1 - Math.pow(friction, n)) / (1 - friction);


alert(velocity_n);
alert(position_n);

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