Derivative Applications And Determining the Function properties Two race cars ar

Question

Derivative Applications And Determining the Function properties

Two race cars are battling which one accelerates faster. Initially, they are still. They drive straightforward. There is more power in the car 1 - it accelerates away from car 2 at first. However, car 2 continue accelerating for longer time and, eventually, it will achieve the same velocity as car 1 and finally it will even reach car 1 on the track. The distance driven by the cars can be expressed as a function of time as follows (distance as meters, time as seconds): s(t) = 2.3 t2-0.05 t3, s2(t) = 1.9t2-0.03 t3 (a) At which time has the car 2 obtained the same velocity as car 1? (b) How long distance have the cars driven by this time? (a) ONE DECIMAL! (b) accuracy of one meter. (a) t- (b) Car 1 m Car 2: Check

Explanation / Answer

velocity of first car,ds1/dt,v1=4.6t-0.15t2

velocity of second car,ds2/dt,v2=3.8t-0.09t2

v1=v2

4.6t-0.15t2=3.8t-0.09t2

0.8t=0.06t2

t=13.3s

b.s1(13.3)=398m, s2(13.3)=331m

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