Kinematics: straight-line or linear motion

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.