2. Part 1 Motion in Two Dimensions

3. Scalars A scalar is a quantity that can be completely described by a single value called magnitude. Magnitude means size or amount and always includes units of measurement. Temperature is a good example of a scalar quantity.

4. Vectors Sometimes a single number does not include enough information to describe a measurement. A vector is a quantity that includes both magnitude and direction.

5. Describing a vector You can describe a vector three ways; –With a vector diagram drawn to scale –As a magnitude-angle pair –As an x-y pair

6. A vector’s direction A vector’s direction is often given using words. Directional words include left, right, up, down, north, south, east, and west. Which coordinates you use depends on the problem you are trying to solve. Sometimes you will make x horizontal and y vertical. Other times, you should choose x to be east and y to be north.

7. Velocity is speed with direction, so velocity is a vector. As objects move in curved paths, their velocity vectors change because the direction of motion changes. The symbol is used to represent velocity. The arrow tells you it is the velocity vector, not the speed. Velocity vector

8. Suppose a ball is launched at five meters per second at an angle of 37 degrees. At the moment after launch the velocity vector for the ball is written as = (5 m/s, 37°) or v = (4, 3) m/s. Both representations tell you exactly how fast and in what direction the ball is moving at that moment. The x-component tells you how fast the ball is moving in the x-direction. The y-component tells you how fast it is moving in the y-direction.

9. Magnitude of the velocity vector The magnitude of the velocity vector is the speed of the object. The ball in the example is moving with a speed of 5 m/s. Speed is represented by a lower case v without the arrow. When a velocity vector is represented graphically, the length is proportional to speed.