/7/ changing velocity

basic principles

• So far we've created an object that only moves in a straight line.
• This foundation can easily be extended.
• Suppose, for example, we want to change our object's speed or direction.
• Remember that velocity is a speed with a direction, so a change to the object's speed or direction is a change to the object's velocity.
• To describe a change in velocity, we use another basic physics concept, acceleration.
• Acceleration is the rate at which an object changes velocity.
• In other words, acceleration describes how much an object's velocity will change during a given amount of time:
  acceleration = change in velocity / time
• The "change in velocity" is described as a vector, with a magnitude and a direction.
• For example, suppose an object has an initial velocity of 10 meters per second at a 45 degree angle.
• Every second, the object changes velocity by 3 meters per second at a 160 degree angle.

• After one second passes, how do we determine the position of the object?
• We add the velocity vector and the acceleration vector together.

• Easy enough to understand in a diagram, but how do we translate adding vectors into something we can use in Flash?
• Remember how we found the horizontal and vertical components of a velocity vector:

• vertical component = sin(direction) * magnitude
• horizontal component = cos(direction) * magnitude
• To add an acceleration vector to a velocity vector, we simply find the components of the acceleration vector and add them to the components of the velocity vector:
  finalX = velX + accelX
finalY = velY + accelY

the code

• We won't have time to walk through the code for movement with acceleration, but you can work through it on your own, below.
• Notice that the only changes are to the moveClip() function.
• In this version of the code, we retrieve the acceleration vector magnitude and direction through text-field inputs.
• If we were to change those inputs to the arrow keys...bang, we'd have ourselves a spaceship!
  // Initialize movement direction, speed, and start time.
function init () {
  velMagnitude = 30; // Total pixels to travel per second
  velDirection = 250; // Angle of object, measured
                    // counterclockwise from the positive x-axis

  lastX = 225; // Object's initial x-coordinate
  lastY = 200; // Object's initial y-coordinate

  // Convert angle to radians so we can
  // use it with Math.cos and Math.sin.
  var radians = degreesToRadians(velDirection);
  // Pixels to move horizontally each second
  moveX = Math.cos(radians) * velMagnitude;
  // Pixels to move vertically per second
  oveY = Math.sin(radians) * velMagnitude;

  // The current time
  now = getTimer();
}

// Function to move a clip with each passing frame.
function moveClip (theClip) {
  // Determine how much time has passed
  then = now;
  now = getTimer();
  elapsed = now - then;
  numSeconds = elapsed / 1000;

  // Set the acceleration vector based on input text fields
  accelMagnitude = isFinite(Number(accelMagnitudeInput)) ? Number(accelMagnitudeInput) : 0; // Pixels of acceleration per second
  accelDirection = isFinite(Number(accelDirectionInput)) ? Number(accelDirectionInput) : 0; // Angle of acceleration

  // Calculate the x and y components of the acceleration vector
  var radians = degreesToRadians(accelDirection);
  // Pixels to accelerate horizontally each second
  accelX = Math.cos(radians) * accelMagnitude;
  // Pixels to accelerate vertically per second
  accelY = Math.sin(radians) * accelMagnitude;

  // Determine the new horizontal location
  // of the clip, based on elapsed time and acceleration.
  moveX += accelX * numSeconds;
  newX = lastX + moveX * numSeconds;

  // Determine the new vertical location
  // of the clip, based on elapsed time and acceleration.
  moveY += accelY * numSeconds;
  newY = lastY - moveY * numSeconds;

  // Place the clip in the appropriate location.
  theClip._x = newX;
  theClip._y = newY;

  // Remember where we placed the clip for next time.
  lastX = newX;
  lastY = newY;
}

// Converts degrees to radians.
function degreesToRadians(degrees) {
  return (degrees/180) * Math.PI;
}