Velocity, Acceleration & Friction

Moving a character by setting its position directly feels robotic: it starts and stops instantly. Real movement — and good-feeling game movement — has momentum. The trick is a chain of three vectors: acceleration changes velocity, velocity changes position.

Position, velocity, acceleration

• Position (px) — where the object is.
• Velocity (px/s) — how fast and in which direction position changes.
• Acceleration (px/s²) — how fast velocity changes. Input, gravity, explosions and thrusters are all accelerations.

function update(dt) {
  const input = normalize(readArrowKeys())
  ship.acc = scale(input, ACCEL)                    // 1. forces → acceleration
  ship.vel = add(ship.vel, scale(ship.acc, dt))     // 2. acceleration → velocity
  ship.vel = scale(ship.vel, 1 - FRICTION * dt)     // 3. friction slows us down
  if (length(ship.vel) > MAX_SPEED)                 // 4. cap the top speed
    ship.vel = scale(normalize(ship.vel), MAX_SPEED)
  ship.pos = add(ship.pos, scale(ship.vel, dt))     // 5. velocity → position
}

This step-by-step update is called Euler integration: each frame we nudge velocity by acceleration × dt, then position by velocity × dt. It’s not perfectly accurate, but it is simple, fast and what most games use (especially combined with a fixed timestep from lesson 3).

Friction and damping

Without friction, the ship would glide forever (like in space — which is a valid design choice!). Multiplying velocity by a number slightly less than 1 every frame bleeds speed away. Low friction feels slippery like ice, high friction feels tight and responsive.