Vectors and scalars are physical quantities that can be measured. Scalars only have magnitude and no direction, such as distance or speed. Vectors have both magnitude and direction, like displacement or velocity. Velocity is a vector quantity that describes both how fast and in which direction an object is moving. Displacement is also a vector that measures the distance an object has moved from its starting point, including direction. There are two main methods for adding vectors - the triangle method uses the Pythagorean theorem, while the parallelogram method draws the vectors as sides of a parallelogram to find the diagonal resultant vector.

1. VECTORS & SCALARS

2. Common Definitions Scalar: A physical quantity that is a single number. Ex: Distance, speed, energy Vector: A physical quantity that possesses both magnitude and direction. Ex: Displacement, velocity, acceleration.

3. Scalar One: Speed Speed is the measure of how fast an entity is going. Rate at which distance is covered.

4. Scalar One: Speed Instantaneous Speed The speed at any instant. Taking the speed at a random time when someone is driving. Average Speed Average of all instantaneous speeds. (Distance traveled)/(Time of travel) is the equation.

5. Vector One: Velocity Velocity is a vector – it has magnitude & direction. Velocity can be measured by using a speedometer in combination with something that indicates the instantaneous direction of travel.

6. Scalar Two: Distance Distance is a scalar quantity. It is the space between two points. The equation for finding distance: d = vit + 1/2at² d – distance, a – acceleration vi – intial velocity, t – time

7. Vector Two: Displacement Displacement has both direction and magnitude: is a vector quantity. It is describing how much distance has been covered from beginning to end. Displacement is measured by mechanically measuring distance.

8. Vector Addition The addition of two vectors. Result of vector addition is known as the resultant. Resultant is the diagonal of the rectangle described in some cases.

9. Triangle Method Basically done using the pythagorean theorem. a²+b²=c², using each side of equation. Ex: two vectors, each 3m. 3²+3²=c² 3√2 is the resultant. Answers can be radical.

10. Parallelogram Method The vectors need to all point in the same direction. Resultant: Diagonal. Start at same point as the vectors.

11. End.