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Mechanics of Motion: Speed, Velocity, and Acceleration Explained

Explore the study of motion in mechanics, including scalar vs. vector quantities, distance vs. displacement, speed vs. velocity, and acceleration. Learn how to graph motion and interpret position, velocity, and acceleration vs. time graphs.

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Mechanics of Motion: Speed, Velocity, and Acceleration Explained

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  1. MOTION Scalar vs. Vector Distance vs. Displacement Speed vs. Velocity Acceleration Graphing Motion

  2. MECHANICS • Study of motion and what produces and affects the motion. • Two types: • Kinematics : Description of motion w/o the cause • Dynamics: Causes of motion

  3. SCALAR Has magnitude NO direction e.g. distance, speed VECTOR Has magnitude Has direction e.g. displacement, velocity SCALAR VS. VECTOR

  4. DISTANCE (x) Total path traveled How far Units: m, cm, km Scalar DISPLACEMENT (x) Straight-line distance between two points…shortest path How far and in what direction Units: m, cm, km Vector DISTANCE VS. DISPLACEMENT

  5. EXAMPLE: A B C Determine the displacement/ distance for the following: • A + B • B + C • A + B + C • A = 10 meters • B = 13 meters • C = 7 meters

  6. How fast Total distance per total time s = x / t Units: m/s, km/hr Scalar Average speed = total distance /total time Instantaneous speed = speed at any instant in time Constant speed = no change in speed SPEED

  7. How fast and in what direction Rate at which object changes direction Change in distance per change in time V = Δx / Δt Units: m/s, km/hr Vector Average velocity = displacement/time Instantaneous velocity VELOCITY

  8. SPEED VS. VELOCITY

  9. HOW TO CHANGE VELOCITY • Speed changes • Direction changes • Both of the above

  10. EXAMPLE: On your way to campus one morning, you walk at 3 m/s east towards campus. After exactly one minute you realize that you've left your physics assignment at home, so you turn around and run, at 6 m/s, back to get it.

  11. EXAMPLE CON’T • Determine the average speed and average velocity. • Total time traveled: 90 seconds • Distance covered at 3 m/s: 180 m. • Distance covered at 6 m/s: 180 m • Avg speed = distance/elapsed time = 360/90 = 4 m/s. • Avg velocity = displacement/elapsed time = 0 m/s. • The instantaneous speed is simply the magnitude of the instantaneous velocity.

  12. ACCELERATION • Rate at which an object changes its velocity • Changing how fast an object is moving • a = v / t • Units: m/s/s = m/s2, km/hr/hr = km/hr2 • Vector • Average acceleration • Instantaneous acceleration • Constant acceleration means velocity changes at constant rate • Zero acceleration means constant or zero velocity

  13. SLOWING DOWN OR SPEEDING UP • Velocity and acceleration are in the same direction (positive or negative)…then it is speeding up. • Velocity and acceleration are in the opposite direction…then it is slowing down.

  14. SLOWING DOWN OR SPEEDING UP

  15. SLOWING DOWN OR SPEEDING UP

  16. There is a difference between negative acceleration and deceleration: Negative acceleration is acceleration in the negative direction as defined by the coordinate system. Deceleration occurs when the acceleration is opposite in direction to the velocity. SLOWING DOWN / SPEEDING UP

  17. MOTION • No Motion • Zero velocity • Zero acceleration • Uniform Motion • Constant velocity • Zero acceleration • Uniform Accelerated Motion • Velocity changes at a constant rate • Constant acceleration

  18. MOTION GRAPHS POSITION VS. TIME

  19. MOTION GRAPHS VELOCITY VS. TIME

  20. MOTION GRAPHS ACCELERATION VS. TIME

  21. MOTION GRAPHS • Position vs. time • Velocity vs. time • Acceleration vs. time SLOPE AREA UNDERTHECURVE

  22. TYPE 1 GRAPHS

  23. TYPE 1 GRAPHS

  24. POSITION-TIME GRAPHS • Slope goes up…velocity gets more positive • Slope goes down…velocity gets more negative • Slope is constant…straight line…constant velocity • Slope is horizontal…zero velocity • Slope is changing….curved line…velocity is changing…acceleration is occurring

  25. Position-Time Graph x 0 t In a given unit of time, the distance covered is the same…constant velocity Upward slope: positive Downward slope: negative Velocity-Time Graph v 0 t Since velocity is constant…line must be horizontal…NOT zero. MOTION GRAPHS

  26. Position-Time Graph x 0 t In a given unit of time, the distance covered is the zero…only time is moving…ZERO velocity Velocity-Time Graph v 0 t Since velocity is ZERO…line must be horizontal…AT zero. MOTION GRAPHS

  27. Position-Time Graph x 0 t In a given unit of time, the distance covered is changing…velocity is NOT constant Velocity-Time Graph v 0 t Since velocity is NOT constant…line diagonal MOTION GRAPHS

  28. time Interpreting Graphs • Horizontal lines represent a stationary object. • Straight lines representconstant speed or velocity • Curving lines represent increasing or decreasing velocity.

  29. time Instantaneous Speed • For a curve, we can find the tangent to the curve at a given point, and then find the slope of the tangent line. • A speedometer shows instantaneous speed.

  30. TYPE 1 GRAPHS

  31. TYPE 1 GRAPHS

  32. TYPE 1 GRAPHS

  33. TYPE 1 GRAPHS

  34. TYPE 2 GRAPHS

  35. TYPE 2 GRAPHS

  36. MAGIC CIRCLE

  37. TYPE 2 GRAPHS

  38. TYPE 2 GRAPHS

  39. TYPE 2 GRAPHS

  40. TYPE 2 GRAPHS

  41. TYPE 2 GRAPHS

  42. TYPE 2 GRAPHS

  43. TYPE 2 GRAPHS

  44. TYPE 2 GRAPHS

  45. Velocity-Time Graph v 0 t In a given unit of time, the velocity remains constant…ZERO acceleration Acceleration-Time Graph a 0 t NO change in velocity Velocity-Time Graphs

  46. Velocity-Time Graph v 0 t In a given unit of time, the velocity is ZERO…ZERO acceleration Acceleration-Time Graph a 0 t Velocity is ZERO Velocity-Time Graphs

  47. Velocity-Time Graph v 0 t In a given unit of time, the velocity is changing… acceleration is NOT zero Acceleration-Time Graph a 0 t Since velocity is changing acceleration is NOT zero Velocity-Time Graphs

  48. MOTION

  49. TYPE 3 GRAPHS

  50. TYPE 3 GRAPHS

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