2 11.1 DISTANCE AND DISPLACEMENT In order to describe motion, a frame of reference is needed. A frame of reference is a system of objects that are not moving in respect to each other.
3 Relative motion is movement in relation to a frame of reference Relative motion is movement in relation to a frame of reference. For example a train that passes people standing on a platform is moving where as passengers on the train appear to not move.
4 MEASURING DISTANCEThe length of a path between two points is distance. When measuring distance it is necessary to find units that are best suited for the distances being measured. The SI unit for measure is the meter.
5 For example the length of the Mississippi River is better measured in kilometers rather than meters but the distance a marble rolls would best be measured in centimeters than meters.
6 MEASURING DISPLACEMENTS Displacement is measured by finding the direction and distance between the starting point and the ending point.
7 The distance that a roller coaster travels would equal the length of the track from start to finish but the roller coasters displacement would be zero because the starting point and finishing point are the same place.
8 COMBINING DISPLACEMENTS Displacement is an example of a vector. A vector is a magnitude and direction. The magnitude can be size, length, or amount. Arrows on a graph or map are used to show vectors. The length of an arrow shows the magnitude of the vector.
9 Vector addition is the combining of vector magnitudes and direction Vector addition is the combining of vector magnitudes and direction. When determining vector along a straight line, all that needs to be done is to add the two displacements.
10 If the vector backtracked along the line, that displacement would be subtracted. The total displacements would be the same as the vector. When it isn’t along the same line, the displacements added together may not equal the vector.
11 11.2 SPEED AND VELOCITYSpeed is the ratio of the distance an object moves to the amount of time the object moves. The SI unit for speed is meters per second (m/s).
12 However, it may be necessary to chose units that are appropriate for what is being measured. There are two ways to express speed: instantaneous and average speed. Average speed is equal to the total distance divided by the total time.
14 The formula is on page 333. This equation is for the entire trip The formula is on page This equation is for the entire trip. Instantaneous speed is the speed at a particular point in time. Your car’s speedometer gives you instantaneous speed. It is the rate an object is moving at a given moment in time.
15 GRAPHING MOTIONThe slope of a line on a distance-time graph is equal to the speed. Note the graphs on page 334.
16 VELOCITYVelocity is the speed and direction an object is moving. Velocity is a vector. If graphing a vector, the vectors with greater speeds would be longer.
17 A change in velocity occurs when there is a change in speed, or direction, or both. An object traveling at a constant speed in the same direction is traveling at constant velocity. If it changes direction, then it’s a change in velocity.
18 COMBINING VELOCITIESVector addition can be used to combine two or more velocities. See the examples on page 337.
19 11.3 ACCELERATIONAcceleration is the rate at which velocity changes. It can be described as changes in speed, changes in direction, or changes in both. Acceleration is a vector.
20 Acceleration can be an increase or also a DECREASE in speed Acceleration can be an increase or also a DECREASE in speed. When an object falls to Earth, it is constantly accelerating. This is called free fall. Free fall is the movement of an object toward Earth solely because of gravity. Objects fall to earth at an acceleration of 9.8 m/s2.
21 Acceleration can occur due to a change in direction Acceleration can occur due to a change in direction. A horse on a carousel is moving at a set speed but because it is constantly changing direction, it is accelerating.
22 Constant acceleration occurs when there is a constant change in velocity. A jet at take off would have constant acceleration.
23 CALCULATING ACCELERATION The formula for calculation acceleration of an object traveling in a straight line is on page 345.
24 An object moving in the same direction at a constant speed is not accelerating. If the object turns a corner then it is accelerating because there is a change in velocity. If an object is gaining speed the acceleration is positive. If it is slowing down it is negative.
25 GRAPHS OF ACCELERATED MOTION SPEED-TIME GRAPHSA slope of a speed-time graph is the acceleration. If a speed-time graph is of an object that is constantly gaining speed, it will appear as a straight line.
26 An example of this linear graph is on page 347 figure 16 An example of this linear graph is on page 347 figure 16. Figure 17 shows an object traveling at constant speed and then slowing down.
27 DISTANCE- TIME GRAPHSAn accelerated object will appear as a curved line on a distance-time graph. An example of this nonlinear graph is on page 348.
28 INSTANTANEOUS ACCELERATION Velocity at a given point in time is instantaneous acceleration.