STEM Fuse GAME:IT Unit 2

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1 STEM Fuse GAME:IT Unit 2 Key formulas for math & physics calculations used in game development Definition of velocity Velocity is similar to speed but it has direction. Let's recap what a speed is. Speed is the rate at which something is moving. For example, a swimmer may swim at the speed of 1 meter per second but he or she swims at the velocity of 1 meter per second east. By specifying that he or she swims in the eastwardly direction, you are defining the velocity he or she swims at. So, when you measure velocity, remember to report both speed and direction, the two components of velocity. Velocity formula Since velocity has direction, it is referred to in Physics as a vector quantity. A vector quantity means it is directional as opposed to a scalar quantity which is what speed is. The formula of velocity used in physics is the same as the formula used for measuring average speed per direction. Let's examine how the velocity formula works. In the diagram above, the three velocities represented are A, B, and C. A is the speed measured in the Eastward direction, B is the speed measured in the south-eastern direction and C is the speed measured in the Northeast direction. For example, velocity A is 10 m/s east, V is 20 m/s southeast and C is 15 m/s northeast. That's it. The velocity is measured in meter per second, the same SI unit as speed. Just remember to specify direction when reporting the velocity.

2 Speed Formula One way to calculate the average speed is to use math formula for speed. Speed formula is also known as average speed formula or speed distance formula or the formula for time distance and speed. Before we calculate the speed at which the lady below is running, let's define what speed is. Then we can calculate how fast the lady below is running or the average speed at which she is running at. Definition of speed Speed is an expression of the rate at which an object moves relative in a frame of reference. That means when you are calculating an average speed of something, you are assuming that the object is moving at a rate relative to a stationary place. For example, the speed of a car is the rate at which the car is moving assuming that the road is stationary or non moving, even though technically the road is moving with the Earth. Physics formula for speed The math formula for speed is distance divided by time. Or simply put, the average speed or how fast something is moving is the distance it has travelled divided by the time it takes to travel. For example, the average speed at which the lady in the picture was running was given by the distance she has run divided by the time it took her to run that distance. Speed is scalar When calculating average speed, note that speed is a scalar and not a vector. By scalar, we mean speed has no direction, unlike another physics term called the Velocity which has a direction. In another word, the speed at which a car is moving East at, say, 5 meters per second is the same as the speed at which the same car is moving West at 5 meters per second. This makes calculating the average speed easy. The last thing we are going to mention about calculating speed is the unit of speed. What is the SI unit for speed? A standard unit for speed in America is miles per hour (mph) or kilometers per hour (kph) in many foreign countries.

3 Acceleration Formula We have discussed speed and velocity, now we are going to discuss acceleration. First of all, we are going to define what an acceleration often used in physics is and then we are going to discuss the acceleration formula. Definition of acceleration Acceleration is an expression of the change in the velocity of an object. Since the velocity has two component; speed and direction, the change can be in speed, direction or both speed and direction. Since the acceleration is defined as the change in velocity, the acceleration is a vector quantity (as opposed to a scalar quantity) meaning acceleration is directional. Finding acceleration Suppose you have a car that goes from 0 miles per hour to 60 miles per hour in 5 seconds. In standard unit, the speed 60 miles per hour is approximately 26.8 meter per second. Suppose also that the acceleration is constant going from 0 m/s to 26.8 m/s in one direction. Then the acceleration is the change in speed or 5.36 m/s 2. Notice that the unit for acceleration is meter per second squared because the acceleration is the rate of change in velocity. That's it. This is the easy way to calculate acceleration - just measure the change in velocity and divide that by the time taken to change the velocity.

4 Newton's Laws of Motion Newton's Laws or Newton's Laws of Motions were invented by the famous English mathematician, physicist, and astronomer Sir Isaac Newton. Among many other great discoveries, Sir Isaac Newton formulated three laws of motion known as Newton's three laws of motion which are still widely used today. The Newton's Laws of Motion revolutionized science of the 17th Century. About Sir Isaac Newton, the man who invented Newton's Laws of Motion Isaac Newton was born on December 25, 1642 in Woolsthorpe, Lincolnshire, England, He attended Trinity College, Cambridge University where the story of the apple falling onto his head giving him the idea for his Newton's Laws of Motion supposedly took place. Three Newton's Laws of Motion The Newton's 3 laws of motion are: the law of inertia, the law of acceleration and the law of reciprocal actions. The first Newton's law of motion or the law of inertia states that an object is at rest unless acted on by a force or an object moving at a constant speed will continue to move at that speed unless acted on by a force. The 2nd law of motion introduces the formula Force equals mass times acceleration. The third law follows the law of conservation of momentum used widely in mathematics and states that each action has an equal and opposite reaction.

5 Newton's First Law Newton's First Law or Newton's First Law of Motion is the first of Newton's Three laws of motion invented by Sir Isaac Newton, one of the greatest mathematician, physicist, and astronomer. Newton's First Law is sometimes known as the Law of Inertia. What is Newton's First Law of Motion? Newton's First Law of Motion states 2 things. First part of Newton's First Law of Motion The first of Newton's First Law of Motion states that sunless acted on by an outside force, an object at rest, stays at rest. Second part of Newton's First Law of Motion The second part of Newton's First Law of Motion states that unless acted on by an outside force, an object moving with uniform velocity continues to move at that velocity. So, in the above picture, the golden ball moves at the velocity of 5 m/s so unless there is an outside force acting on it, it will continue to move at 5 m/s. In reality, though, a ball moving at a velocity will eventually come to a stop because it is acted on by many forces such as air resistance.

6 Newton's Second Law Newton's Second Law or Newton's second law of motion is probably the most famous of all of Newton's three laws of motion. Newton's second law of motion introduces one of the most famous mathematical or physics formula concerning mass, force and motion. So, what is this Newton's Second Law of Motion? Formula for Newton's Second Law of Motion Newton's 2nd law of motion states that if an object of mass m which is measured in kilograms is acted on by a force of magnitude F measured in Newtons, the magnitude of the acceleration a (measured in meters per second squared) can be found according to the physics formula F equals m times a or Force is Mass times Acceleration. Unit of force Force is measured in Newton which is the standard unit of mechanical force. The unit Newton is often written as capital N. What does one Newton of force mean? One Newton (N) of force is the force that it takes to make a mass of 1 kilogram accelerate at a rate of 1 meter per second squared. Since Force is mass multiplied by acceleration, the Newton is really kilogram, meter per second squared. But, all you really need to remember is that Force is measured in Newton. That's it. Newton's 2nd Law of Motion is given by F equals m times a or mass times acceleration measured in Newton.

7 Newton's Third Law Newton's Third Law or Newton's third law of motion is the last of the Three Newton's Laws of Motion invented by famous and brilliant mathematician, physicist and astronomer, Sir Isaac Newton. The Three Newton's Laws of Motion shaped how we understand the world. What is Newton's Third Law of Motion? Newton's 3rd Law of Motion states that for every action, there is an equal and opposite reaction. In another word, if there is a Force F on the surface of an object such as the golden ball above, then there is an equal and opposite force exerted back at the same point. This equal and opposite force is often given by negative F. In the diagram above, when the boxer kicks the golden ball with a force F, there is an equal and opposite force (-F) being applied back at his foot. To sum up Newton's Third Law of Motion: Formula for Newton's Third Law of Motion That's it. Action equals reaction is the Famous Newton's 3rd Law of Motion.