A person driving her car at 47 km/h approaches an intersection just asthe traffi

Question

A person driving her car at 47 km/h approaches an intersection just asthe traffic light turns yellow. She knows that the yellow lightlasts only 2.0 s before turning to red, and she is 30 m away fromthe near side of the intersection (Fig. 2-29). The intersection is15 m wide. Her car's maximum deceleration is -5.6 m/s2, whereas it canaccelerate from 47 km/h to70 km/h in 6.9 s. Ignore thelength of her car and her reaction time.
1) Ifshe hits the brakes, how far will she travel beforestopping? 2)If shehits the gas instead, how far will she travel before the lightturns red? 3)Should shetry to stop, or should she speed up to cross the intersectionbefore the light turns red?
1) Ifshe hits the brakes, how far will she travel beforestopping? 2)If shehits the gas instead, how far will she travel before the lightturns red? 3)Should shetry to stop, or should she speed up to cross the intersectionbefore the light turns red?

Explanation / Answer

1) vi = 47km/h = 47*1000m/3600s = 13.06m/s,vf = 0 let s be the travel distance after hit the brake, wehave: vf2-vi2 =2as s = (vf2-vi2)/2a =(0-(13.06m/s)2)/(2*(-5.6m/s2) = 15.23m she will stop after s = 15.23m 2) distance d = vit + (1/2)at2, (1) she get only 2.0s, so t=2.0s since the car can accelerate from 47 km/h to 70 km/h = 70*1000m/3600s =19.44m/s in 6.9 s, we have: vf = 19.44m/s = 13.06m/s + at a = (19.44m/s - 13.06m/s)/6.9s = 0.92m/s2 substitue a into (1), we have: d = 13.06m/s*2.0s +(1/2)*0.92m/s2(2.0s)2 = 27.96m she only travel 27.96m. 3. she should stop before she will able to stop well before thetraffic light (less than 30m) but she will not able to pass before the light turn red. substitue a into (1), we have: d = 13.06m/s*2.0s +(1/2)*0.92m/s2(2.0s)2 = 27.96m she only travel 27.96m. 3. she should stop before she will able to stop well before thetraffic light (less than 30m) but she will not able to pass before the light turn red.

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