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Linear Motion

Linear Motion. Chapter 3. Vectors vs Scalars. Scalars are quantities that have a magnitude, or numeric value which represents a size i.e. 14m or 76mph. Vectors are quantities which have a magnitude and a direction, for instance 12m to the right or 32mph east. Distance d Scalar

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Linear Motion

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  1. Linear Motion Chapter 3

  2. Vectors vs Scalars • Scalars are quantities that have a magnitude, or numeric value which represents a size i.e. 14m or 76mph. • Vectors are quantities which have a magnitude and a direction, for instance 12m to the right or 32mph east.

  3. Distanced Scalar Standard units are meters A measure of how far you have moved with respect to you (what a pedometer would measure) Displacementd Vector Standard units are meters accompanied by direction. A measure of how far you are with respect to where you started (or change in position). Describing how far you’ve gone

  4. Distance vs Displacement • The person, according to a pedometer has walked a total of 12m. That is the distance traveled. • The person walking starts where she stops, so her displacement is zero.

  5. Speedv Scalar Standard unit is m/s Velocityv Vector Standard unit is m/s, plus direction Measuring how fast you are going

  6. If it takes the person 4 seconds to walk around the square, what is her average speed and average velocity? For speed, d=12m and t=4s, so v=3m/s For velocity, d=0 and t=4s, so v=0m/s Velocity and Speed

  7. Average velocity/speed A value summarizing the average of the entire trip. All that’s needed is total displacement/distance and total time. Instantaneous velocity A value that summarizes the velocity or speed of something at a given instant in time. What the speedometer in your car reads. Can change from moment to moment. Different types of velocity and speed

  8. Acceleration • Change in velocity over time. • Either hitting the gas or hitting the break counts as acceleration. • Units are m/s2 • delta. • Means “change in” and is calculated by subtracting the initial value from the final value.

  9. Using linear motion equations • We always assume that acceleration is constant. • We use vector quantities, not scalar quantities. • We always use instantaneous velocities, not average velocities • Direction of a vector is indicated by sign. Incorrect use of signs will result in incorrect answers.

  10. The Big 4

  11. Problem Solving Steps • Identify givens in a problem and write them down. • Draw a sketch of situation • Determine what is being asked for and write down with a question mark. • Select an equation that uses the variables (known and unknown) you are dealing with and nothing else. • Solve the selected equation for the unknown.

  12. Gravity • Gravity causes an acceleration. • All objects have the same acceleration due to gravity. • Differences in falling speed/acceleration are due to air resistance, not differences in gravity. • g=-9.8m/s2 • When analyzing a falling object, consider final velocity before the object hits the grounds.

  13. Hidden Variables • Objects falling through space can be assumed to accelerate at a rate of –9.8m/s2. • Starting from rest corresponds to a vi=0 • A change in direction indicates that at some point v=0. • Dropped objects have no initial velocity.

  14. Displacement (Position) vs. Time Graphs • Position, or displacement can be determined by reading the graph. • Velocity is determined by the slope of the graph (slope equation will give units of m/s). • If looking for a slope at a specific point (i.e. 4s) determine the slope of the entire line pointing in the same direction. That will be the same as the slope of a specific point. What is the velocity of the object at 4 seconds?

  15. Velocity vs. Time Graphs • Velocity is determined by reading the graph. • Acceleration is determined by reading the slope of the graph (slope equation will give units of m/s2).

  16. Velocity vs. Time Graphs • Displacement is found using area between the curve and the x axis. This area is referred to as the area under the curve (finding area will yield units of m). • Areas above the x axis are considered positive. Those underneath the x axis are considered negative. • Break areas into triangles (A=1/2bh), rectangles (A=bh), and trapezoids (A=1/2[b1+ b2]h).

  17. Velocity vs. Time Graphs • What is the acceleration of the object at 6s? • What is the displacement of the object at 4s? • What is the displacement of the object from 3s to 12s?

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