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Kinematics using anti-differentiation

Calculus HOME | Achievement Objectives | Gradient | Gradient Functions | Differentiation | Gradient at a point | Find point with gradient | Equation of Tangent | Second Derivitive | Coordinates of Max & Min | Increasing, Decreasing Functions | Applications | Kinematics with differentiation | Antidifferentiation | Finding 'C' | Kinematics with anti-differentiation | Rates of Change | Mixed Problems | Revision

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Kinematics - again

Using anti-differentiation to find a rule for distance, from a given speed function or a rule for speed from a given acceleration function.

Using additional information (eg a given distance at a set time) to determine the value for 'C'

Interpreting the meaning of positive and negative speed (and acceleration)

Class Notes | Blank Notes

Ex17.03, 17.04

NuLake p99, 100

 

 

Mouse over below

Distance function S=

 

 

Speed function V=

 

 

Acceleration Function A=

 

Note: remember then integrating constant 'C' needs to be found when integrating

 

Find the distance function of a car, given the speed function is defined by v = 6t2 + 4t + 5 and the car is at a distance of 28m when t = 3 sec

Steps:

v = 6t2 + 4t + 5

1) Anti differentiate to find 'distance' function

d = 2t3 + 2t2 + 5t + c

2) Substitute in d = 28 and t = 3 to find 'c'

d = 2t3 + 2t2 + 5t + c
28 = 2x33 + 2x32 + 5x3 + c
28 = 54 + 18 + 15 + c
28 = 88 + c
c = -60

3) The distance function

d = 2t3 + 2t2 + 5t - 60

 

Class Notes | Blank Notes Screen snaps

 

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