spoiler

vector.kt

import kotlin.jvm.JvmStatic
import kotlin.math.sqrt

data class Vector2D(val x: Double, val y: Double) {

    val length: Double
        get() = sqrt(x * x + y * y)

    val normalized: Vector2D
        get() = check(this != ZERO) { "Zero length vector can't be normalized" }.let { this / length }

    operator fun plus(other: Vector2D): Vector2D = Vector2D(x + other.x, y + other.y)

    operator fun minus(other: Vector2D): Vector2D = Vector2D(x - other.x, y - other.y)

    operator fun unaryMinus(): Vector2D = Vector2D(-x, -y)

    operator fun times(a: Double): Vector2D = Vector2D(x * a, y * a)

    private operator fun div(a: Double): Vector2D = Vector2D(x / a, y / a)

    operator fun Double.times(vector: Vector2D) = vector * this

    companion object {
        @JvmStatic
        val ZERO = Vector2D(0.0, 0.0)
    }
}

fun Vector2D.changeSpeed(value: Double): Vector2D = normalized * (length + value)