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Kinematics: straight-line or linear motion

Kinematics: straight-line or linear motion. Distance vs. Displacement. Distance indicates how far an object moves. Displacement indicates the change of position of an object when it moves. Distance has magnitude (a number value + a unit of measure). Example: 3 m

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Kinematics: straight-line or linear motion

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  1. Kinematics: straight-line or linear motion

  2. Distance vs. Displacement • Distance indicates how far an object moves. • Displacement indicates the change of position of an object when it moves. • Distance has magnitude (a number value + a unit of measure). Example: 3 m • Displacement has magnitude and direction. Example: 3 m, east

  3. Symbols & Units • Both distance and displacement can be represented by a variety of symbols in an equation: d, Δd, Δx, or Δy (Note: The Greek letter deltaΔ means “change of” as in “change of position” or displacement, in other words) • Δd = final position − initial position • Both are measured in SI units of meters (m) or meters with a prefix.

  4. Speed vs. Velocity • Speed indicates how fast something moves. Velocity indicates how fast something moves and in which direction. Direction can be indicated by +/− signs, left/right, north/south, east/west, up/down, or a reference angle. • Both are represented in equations by the lower-case letter v. Both are measured in SI units of m/s.

  5. Average Speed • Average speed = distance travelled/time • vavg= d/t [Note: time can be represented the symbol t or Δt] • Example: How much is the average speed of a car covering 300 m in 6s? • Answer: v = 300 m/ 6s = 50 m/s • Speed provides no indication of direction.

  6. Avg. Velocity = Speed with direction • Average velocity = displacement/time Recall: displacement = change of position • vavg= Δd/t = (df − di)/t = rate of change of position with time • Example: A ball rolls from position -2m to +4 m in 2s. What is the ball’s velocity? • Answer: v = [+4m – (-2m)]/2s = +3 m/s

  7. Instantaneous Speed (Velocity) • Instantaneous speed or velocity indicates how fast something moves at a specific instant in time. Instantaneous speed variesfrom second to second when something speeds up or slows down. • In the case of constant or uniform speed or velocity, there is no variation so the instantaneous speed equals the average speed over a time interval.

  8. Slope of Position vs Time Graph • Avg. velocity v = the slope of the Position vs. Time graph d Here there are three parts to the motion. v = slope = rise/run = Δd/Δt Δd Δt t

  9. Sign & Value of the Slope • The sign of the slope of the Position vs. Time graphindicates the direction of movement. • Positive slope means movement toward the positive direction. • Negative slope means movement toward the negative direction. • Steeper the slope, the faster the motion!

  10. Acceleration—Part 1 • A moving object accelerates if 1) it speeds up, 2) it slows down, or 3) it changes direction. • Avg. acceleration = change of velocity/time • aavg = Δv/Δt = (vf − vi)/ Δt • Acceleration means rate of change of velocity. • Example: What is the acceleration of an arrow launched upward if it changes its velocity from +30 m/s to +10 m/s in 2 s? • a = [+10 m/s − (+30 m/s)]/2s = − 10 m/s2

  11. Acceleration—Part 2 • Notice that acceleration has SI units of m/s2. Look at the equation a = Δv/Δt. Plug in just the units for Δv and Δt and you get (m/s)/s. (m/s)/s is re-written as m/s2. • Acceleration can be a + or − quantity. In fact, the sign indicates the direction of an acceleration. [Later you will learn that accelerations are caused by influences called forces and the direction of an acceleration matches the force causing it.]

  12. Sign of the Acceleration • Whether the sign of the acceleration (indicating direction) means speeding up or slow down depends on the sign of the velocity as well. Simple rule: Same signs, speed up. Opposite signs, slow down. • VelocityAccelerationResult • + + speed up • − − speed up • + − slow down • − + slow down

  13. Zero Acceleration means Constant Velocity • An object having zero acceleration means it has a constant velocity. Likewise an object with a constant velocity has zero acceleration. There’s no change in velocity, so there’s no acceleration! Zero, nada, zilch. • Constant velocity on the other hand means either the object is at rest (v = 0 m/s) or it is moving at a constant speed in a straight line.

  14. Constant Acceleration (≠ 0) • Constant or uniform acceleration (≠ 0) means an object steadily speeds up, slows down, or changes direction (in a curved path of some sort). • Constant acceleration is indicated by a straight slanted line on a Velocity vs. Time graph. The slope of the v vs. t graph is the acceleration! • Constant acceleration is indicated by a straight flat line on an Acceleration vs. Time graph.

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