An Introduction to Linear Kinematics

1. An Introduction to Linear Kinematics Linear Kinematics

2. Kinematic Analysis • Linear Kinematics • description of the motion of a body • the appearance of a motion with respect to time • Motion described in terms of (variables): • Distance, displacement, length (e.g. stride, stroke) • Time, cadence (e.g. stride frequency, stroke frequency) • Speed, velocity • Acceleration • Single point models • e.g. Centre of mass (CM) during running/jumping • Multi-segment models • e.g. Co-ordination of body segments during running/jumping

3. Distance & Displacement • Distance: • Length of path which a body covers during motion • Units: metre (m), centimeter (cm), kilometer (km) • Displacement: • The change in position of a body during motion • Units: metre (m), centimeter (cm), kilometer (km) • Distance is a scalar, and displacement is a vector variable

4. If displacement = 50 m If t = 5 s v = 50 / 5 = 10 m·s-1 Speed and Velocity • Speed (scalar) • Length of path (distance) divided by change in time (∆t) • Average velocity (vector) • Change in position (∆p) divided by change in time (∆t) • Displacement (d) divided by change in time (∆t) • Vector equivalent of linear speed

5. Current velocity Swimmer’s velocity Resultant velocity Velocity • Units of velocity • m/s or m·s-1 • Velocity is a vector • Magnitude and direction calculated using Pythagoras and trigonometry • The velocity of a swimmer in a river is the vector sum of the velocities of swimmer and current.

6. Velocity • For human gait, speed is the product of stride length and stride velocity. • Adults walk faster using longer stride lengths and faster stride frequency. • Stride length in children has great variability.

7. Velocity • Runners traveling at a slower pace tend to increase velocity primarily by stride ____? • At faster running speeds, runners rely more on increasing stride ____? • Most runners tend to choose a combination of stride length and stride frequency that minimizes physiological cost. Best sprinters distinguished by high stride ___ & short ground contact time.

8. Velocity Men’s 100-m Dash 1988 Olympic Games • Pace: rate of movement, or established rate of locomotion. • Pace = _time_ distance • Men’s world record marathon pace = 4:37 min/mile (2:03.38) • Women’s world record marathon pace = 5:30 min/mile

9. Average velocity Average velocity not necessarily equal to instantaneous velocity Instantaneous velocity Occurring at one instant in time Like an automobile speedometer Winner of the Men's 100 m at the 2004 Athens Olympics in 9.85 s Average velocity = 100 / 9.85 = 10.15 m·s-1 Velocity 2004 Olympic Men's 100 m

10. Kinematic analysis of 100 m sprint

11. Kinematic analysis of 100 m sprint

12. Average velocity 0-10 m v = d / ∆t = 10 / 2.2 = 4.5 m·s-1 10-20 m = 10 / 1.2 = 8.3 m·s-1 20-30 m = 10 / 0.8 = 12.5 m·s-1 30-40 m = 10 / 0.7 = 14.3 m·s-1 40-50 m = 10 / 0.8 = 12.5 m·s-1 50-60 m = 10 / 0.8 = 12.5 m·s-1 60-70 m = 10 / 0.7 = 14.3 m·s-1 70-80 m = 10 / 0.8 = 12.5 m·s-1 80-90 m = 10 / 0.9 = 11.1 m·s-1 90-100 m = 10 / 0.9 = 11.1 m·s-1 Velocity during 100 m

13. Average Acceleration • Change in velocity (∆v) divided by change in time (∆t) • Units • m/s/s or m/s2 or m·s-2 • Vector • As with displacement & velocity, acceleration can be resolved into components using trigonometry & Pythagorean theorem V1= 4.5 m·s-1 V2= 8.3 m·s-1 ∆t= 1.2 s a = (8.3 - 4.5) / 1.2 = 3.2 m·s-2

14. Acceleration during 100 m Acceleration at start of race a = (v2 - v1) / ∆t = (8.3 - 4.5) / 1.2 Positive Acceleration = 3.2 m·s-2 _________________________________________________________________________________________________________________________________ Acceleration during middle of race a = (v2 - v1)/ ∆t = (12.5 - 12.5) / 0.8 Constant Velocity = 0 _________________________________________________________________________________________________________________________________ Acceleration at end of race a = (v2 - v1)/ ∆t = (11.1 - 14.3) / 0.9 Negative Acceleration = -3.5 m·s-2

15. Acceleration and Direction of Motion • Complicating factor in understanding acceleration is direction of motion of object. • When object moving in same direction continually, accelerate often used to indicate an increase in velocity and decelerate to indicate a decrease in velocity. • If object changes direction, one direction is positive, the opposite direction is negative.

16. Increasing velocity Increasing velocity Positive acceleration Negative acceleration Decreasing velocity Decreasing velocity Negative acceleration Positive acceleration Motion in a positive direction Motion in a negative direction Acceleration Player running in negative direction increases negative velocity results in negative acceleration. Player begins to decrease velocity in negative direction has positive acceleration. Positive and negative accelerations can occur without changing directions.

17. Summary • Variables used to describe motion are either: • Scalar (magnitude only: e.g. time, distance and speed) • Vector (magnitude and direction: e.g. displacement, velocity and acceleration) • Displacement is the change in position of a body • Average velocity is the change in position divided by the change in time • Average acceleration is the change in velocity divided by the change in time

18. Recommended Reading • Enoka, R.M. (2002). Neuromechanics of Human Movement (3rd edition). Champaign, IL.: Human Kinetics. Pages 3-10 & 22-27. • Grimshaw, P., Lees, A., Fowler, N. & Burden, A. (2006). Sport and Exercise Biomechanics. New York: Taylor & Francis. Pages 11-21. • Hamill, J. & Knutzen, K.M. (2003). Biomechanical Basis of Human Movement (2nd edition). Philadelphia: Lippincott Williams & Wilkins. Pages 271-289. • McGinnis, P.M. (2005). Biomechanics of Sport and Exercise (2nd edition). Champaign, IL.: Human Kinetics. Pages 47-62.