# Math B Differentiation Investigation

Topics: Velocity, Acceleration, Kinematics Pages: 16 (5243 words) Published: May 4, 2013
12
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:...