Quantitative Biomechanics

Distance vs Change in Position

• Distance is the path that an object has travelled

• Ex. The distance around a track is 400m

• Position is the straight line measurement from the starting position to the ending position

• Ex. The change in position around a track is 0m

Speed vs Velocity

• Speed is the rate of change of distance

• Velocity is the rate of change of position

• Speed and Velocity in a straight line are the same. Speed and Velocity over a curved path will be different.

Velocity

• Velocity is the rate of change of position• V=(p2-p1)/(t2-t1)• Direction can be included as + or –– Up and Right are position– Down and Left are negative– Be sure about direction if you are using it in various

movements skills as the direction may not be clear– In this case you do not need to include direction in

this way but just in a manner that makes it clear

Acceleration

• Acceleration is the rate of change of velocity• a = (v2-v1)/(t2-t1)• Acceleration can be positive (speeding up) or

negative (slowing down)

• Remember that if mass of an object is consistent then Force and Acceleration are proportional due to F=ma

Sport Books Publisher 6

The greater the force applied to a soccer ball that has the same mass, the greater the ball’s acceleration

Force, mass, and acceleration

Sport Books Publisher 7

As the soccer ball’s mass increases, it experiences less acceleration from a kick of the same force

Force, mass, and acceleration cont.

Sport Books Publisher 8

As the mass of the soccer ball is increased, greater force must be generated if the ball is to have the same acceleration

Force, mass, and acceleration cont.

Graphing

• Position-Time Graphs – Show velocity

• Velocity-Time Graphs– Show acceleration

0

displacement

Graphical analysis of motion

• (i) at rest• (ii) moving with uniform speed

Time0

moving with non-uniform speed

Graphs

Displacement

0Increasing speed

maximum speed

minimum speed (at rest)

Time

Graphical Representations

Velocity

(i)

Time

(ii)

(iii) (iv)

(i) at rest(ii) moving with uniform speed(iii) moving with uniform acceleration(iv) moving with non-uniform acceleration

Other skills that could be useful

– To calculate the area under a speed-time graph to determine the distance travelled for motion with uniform speed or uniform acceleration

– The acceleration of free fall for a body near to the Earth is constant and is approximately 10 m/s2

Area Under the Curve of a Graph

Velocity /m/s

(i)

(ii)

(iii)

Time/s0 10 14 23

A bus stopped at a bus-stop for 10 seconds before accelerating to a velocity of 15 m/s in 4 seconds and then at a constant speed for the next 9 seconds. How does the graph look like?

15

Area Under A Graph

Velocity /m/s

(i)

(ii)

(iii)

Time/s0 10 14 23

A bus stopped at a bus-stop for 10 seconds before accelerating to a velocity of 15 m/s in 4 seconds and then at a constant speed for the next 9 seconds.

15

Area Under A Graph

Velocity /m/s

(i)

(ii)

(iii)

Time/s0 10 14 23

A bus stopped at a bus-stop for 10 seconds before accelerating to a velocity of 15 m/s in 4 seconds and then at a constant speed for the next 9 seconds.

15 How far did the bus go in this 23 seconds?

Why is all this helpful

• Sometimes your eyes can trick you

• Explains how changes in force happen

• The difference between the best and worst players many times is the speed at which movements are done

What do you need to know

• How to calculate :– Speed– Change in position– Velocity– Acceleration

• How to read graphs showing changes in:– Position– Velocity