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# Kinematics using anti-differentiation

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)

Ex17.03, 17.04

#### 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