# Math B Differentiation Investigation

Mathematics 11B

Semester 2 Assignment

Yeri Rim

PART A: THE GREAT COCKROACH RACE

JERSEY NUMBER| NAME| EQUATIONS|

| | DISPLACEMENT (s)| VELOCITY (v)| ACCELERATION (a)|

1| Kenny| s=0.52t| v=0.52| a=0|

2| Kerry| s=0.08tt-4(t-8.45)| v=0.24t2-1.992t+2.704| a=0.48t-1.992| 3| Kevvie| s=0.8t(t-9)| v=1.6t-7.2| a=1.6|

From the given displacement functions of each Kenny, Kerry and Kevvie, the velocity and acceleration functions of each individual was found through the technique of differentiation by rule. Velocity functions are the first derivatives of the displacement functions, and acceleration functions are the first derivatives of the subsequent velocity functions. DIFFERENTIATION OF FUNCTIONS

Velocity

v=dsdt=ntn-1

1. Kenny

s=0.52t

dsdt=0.52

∴v=0.52

2. Kerry

s=0.08tt-4(t-8.45)

dsdt=0.24t2-1.992t+2.704

∴v=0.24t2-1.992t+2.704

3. Kevvie

s=0.8tt-9

dsdt=1.6t-7.2

∴v=1.6t-7.2

Acceleration

a=dvdt=ntn-1

1. Kenny

v=0.52

dvdt=0

∴a=0

2. Kerry

v=0.24t2-1.992t+2.704

dvdt=0.48t-1.992

∴a=0.48t-1.992

3. Kevvie

v=1.6t-7.2

dvdt=1.6

∴a=1.6

| DISPLACEMENT (m)| VELOCITY (m/min)| ACCELERATION (m/min/min)| TIME (min)| Kenny| Kerry| Kevvie| Kenny| Kerry| Kevvie| Kenny| Kerry| Kevvie| 0| 0| 0| 0| 0.52| 2.704| -7.2| 0| -1.992| 1.6|

1| 0.52| 1.788| -6.4| 0.52| 0.952| -5.6| 0| -1.512| 1.6| 2| 1.04| 2.064| -11.2| 0.52| -0.32| -4| 0| -1.032| 1.6| 3| 1.56| 1.308| -14.4| 0.52| -1.112| -2.4| 0| -0.552| 1.6| 4| 2.08| 0| -16| 0.52| -1.424| -0.8| 0| -0.072| 1.6| 5| 2.6| -1.38| -16| 0.52| -1.256| 0.8| 0| 0.408| 1.6| 6| 3.12| -2.352| -14.4| 0.52| -0.608| 2.4| 0| 0.888| 1.6| 7| 3.64| -2.436| -11.2| 0.52| 0.52| 4| 0| 1.368| 1.6| 8| 4.16| -1.152| -6.4| 0.52| 2.128| 5.6| 0| 1.848| 1.6| 9| 4.68| 1.98| 0| 0.52| 4.216| 7.2| 0| 2.328| 1.6| 10| 5.2| 7.44| 8| 0.52| 6.784| 8.8| 0| 2.808| 1.6| Table 1.0 Displacement, Velocity and Acceleration calculated from above equations of each cockroach at each minute of race

f3t=0.8tt-9

f1t=0.52t

f2t=0.08tt-4t-8.45

Graph 1.0 Displacement graph of each cockroach

KEYS:

Kenny: f1t=0.52t

Kerry: f2t=0.08tt-4t-8.45

Kevvie: f3t=0.8tt-9

Race Finish line: f4t=5

(9.608 , 4.99)

f4t=5

f3t=0.8tt-9

f2t=0.08tt-4t-8.45

f1t=0.52t

KEYS:

Kenny: f1t=0.52t

Kerry: f2t=0.08tt-4t-8.45

Kevvie: f3t=0.8tt-9

Graph 1.1 Zoom-in of the end of the race at s=5m

Table 1.1 Displacement, Velocity and Acceleration calculated from above equations of each cockroach at significant moments in the race, collected from Graph 1.0 and Graph 1.1 | DISPLACEMENT (m)| VELOCITY (m/min)| ACCELERATION (m/min/min)| TIME (min)| Kenny| Kerry| Kevvie| Kenny| Kerry| Kevvie| Kenny| Kerry| Kevvie| 0| 0| 0| 0| 0.52| 2.704| -7.2| 0| -1.992| 1.6|

1.71| 0.8892| 2.111453| -9.97272| 0.52| 0| -4.464| 0| -1.1712| 1.6| 2.84| 1.47| 1.47| -13.9955| 0.52| -1.01754| -2.656| 0| -0.6288| 1.6| 4| 2.08| 0| -16| 0.52| -1.424| -0.8| 0| -0.072| 1.6| 4.5| 2.34| -0.711| -16.2| 0.52| -1.4| 0| 0| 0.168| 1.6| 6.59| 3.4268| -2.53973| -12.7055| 0.52| 0| 3.344| 0| 1.1712| 1.6| 8.45| 4.394| 0| -3.718| 0.52| 3.0082| 6.32| 0| 2.064| 1.6| 9| 4.68| 1.98| 0| 0.52| 4.216| 7.2| 0| 2.328| 1.6| 9.6089| 4.9966| 4.9966| 4.673331| 0.52| 5.720143| 8.1728| 0| 2.61984| 1.6| 9.61| 4.9972| 5.003043| 4.68968| 0.52| 5.725384| 8.176| 0| 2.6208| 1.6| 9.62| 5.0024| 5.060428| 4.77152| 0.52| 5.751616| 8.192| 0| 2.6256| 1.6| 9.65| 5.018| 5.23416| 5.018| 0.52| 5.8306| 8.24| 0| 2.64| 1.6|

Table 1.2 Significant moments in the race collected from Graph 1.0 and Graph 1.1 Time (m)| Displacement (m)| Velocity (m/min)| Acceleration (m/min/min)| Description| Relative Placing| 0| Kenny: 0Kerry: 0Kevvie: 0| Kenny: 0.52Kerry: 2.7Kevvie: -7.2| Kenny:...

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