A person driving her car at 40 km/h approaches an intersection just as the traff

Question

A person driving her car at 40 km/h approaches an intersection just as the traffic light turns yellow. She knows that the yellow light lasts only 2.0 s before turning to red, and she is 30 m away from the near side of the intersection (Fig. 2-29). The intersection is 15 m wide. Her car's maximum deceleration is -5.0 m/s2, whereas it can accelerate from 40 km/h to 70 km/h in 9.0 s. Ignore the length of her car and her reaction time.

Figure 2-29
If she hits the brakes, how far will she travel before stopping?
20.28 m
If she hits the gas instead, how far will she travel before the light turns red?
m
Should she try to stop, or should she speed up to cross the intersection before the light turns red?
stop
speed up

Explanation / Answer

if she hits breaks acceleration a = -5m/s2 initial speed u = 40kmph = 40*5/18 m/s = 100/9 m/s final speed v = 0 so, v2 - u2 = 2as =>0 - (100/9)^2 = 2*(-5)*s =>s = 1000/81 m = 12.35m so, applying brakes is safe if she hits the gas acceleration a = [(70 - 40)*5/18]/9 = 150/162 = 50/54 = 25/27 initial speed u = 100/9 m/s time = 2s final speed v = u + at = 100/9 + 2*25/27 = 350/27 m/s v2 - u2 = 2as =>(350/27)^2 - (100/9)^2 = 2*25/27 * s => s = 24.1m she can't cross the intersection by speeding up so, she should stop. plz rate!

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