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18  Kinematics  again
Using antidifferentiation 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) 
Ex17.03, 17.04 NuLake p99, 100 
Distance function S= 



Speed function V= 



Acceleration Function A= 
Find the distance function of a car, given the speed function is defined by v = 6t^{2} + 4t + 5 and the car is at a distance of 28m when t = 3 sec 

Steps: 
v = 6t^{2} + 4t + 5 
1) Anti differentiate to find 'distance' function 
d = 2t^{3} + 2t^{2} + 5t + c 
2) Substitute in d = 28 and t = 3 to find 'c' 
d = 2t^{3} + 2t^{2} + 5t + c 
3) The distance function 
d = 2t^{3} + 2t^{2} + 5t  60 