A person driving her car at 45 km/h approaches an intersection justas the traffi

Question

A person driving her car at 45 km/h approaches an intersection justas the traffic light turns yellow. She knows that the yellowlight lasts only 2.0 sec before turning to red, and she is 28 maway from the near side of the intersection. Should she tryto stop, or should she speed up to cross the intersection beforethe light turns red/ The intersection is 15m wide. Hercar's max deceleration is -5.8m/s2 , whereas it canaccelerate from 45km/h to 65 km/h in 6.0 s. Ignore the lengthof her car and her reaction time.

Explanation / Answer

45 km/h=12.5 m/s 65 km/h=18.06 m/s let acceleration=a v=u+a*t 18.06=12.5+a*6 a=0.93 m/s2 deceleration of the car=-5.8 initial velocity=u=12.5 if the car decelerate for 2 s the velocity of the car after 2s=v v=u-a*t v=12.5-5.8*2 v=0.9 m/s if the car accelerates in 2 s the car will travel s=u*t+(1/2)*a*t2 s=12.5*2+(1/2)*0.93*4 s=26.86 so if he accelerates he will be 1.14 m from the nearest side so it will be better if he decelerates

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