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Distance,Speed,Acceleration!

Distance,Speed,Acceleration!. Speed = change in distance change in time. Acceleration = change in speed change in time. Distance/Time Functions. Suppose a distance/time function is given by d = f(t). then. distance: d = f(t). speed: s = f ´ (t).

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Distance,Speed,Acceleration!

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  1. Distance,Speed,Acceleration! Speed = change in distance change in time Acceleration = change in speed change in time Distance/Time Functions Suppose a distance/time function is given by d = f(t) then distance: d = f(t) speed: s = f´(t) 2nd derivative acceleration: a = f´´(t)

  2. This now means that if we have a “speed/time” function Ie S = f(t) then acceleration = f´(t) and distance =  f(t)dt NB: Integration gives area under curve. In Physics area under speed/time graph = distance .

  3. Example The speed of an object(in m/s) is given by the formula f(t) = 2t2 – 5t (i) Find its speed after10 seconds. (ii) How far did it travel in the first 10 seconds? (iii) Find its rate of acceleration 10s into the journey. ********* (i) f(t) = 2t2 – 5t so f(10) = (2 X 102) – (5 X 10) Speed is 150m/s = 200 - 50 = 150

  4. 10 (ii) d =  f(t) dt 0 =  2t2 – 5tdt 10 0 = [2/3t3 - 5/2t2] 10 0 = (2000/3 – 250) - 0 Distance travelled = 4162/3 m = 4162/3 (iii) f ´(t) = 4t - 5 so f ´(10) = (4 X 10) - 5 = 35 Acceleration = 35m/s/s

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