Question

as a function of time is given by Fig. 2-36. 87. A person driving her car at 45 km/h approaches an intersec tion 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 28 m away from the near side of the intersection (Fig. 51) Should she try to stop, or should she speed up to cross the intersection before the light turns red? The intersection is 15 m wide. Her car's maximum deceleration is 5.8 m/s whereas it can accelerate from 45 km/h to 65 km/h in 6.0 s. Ignore the length of her car and her reaction time. 28 m 15 m FIGURE 2-51 Problem 87.

How do I solve this and what is the correct answer?

Answer 1

maximum decelration = - 5.8 m/s^2

Suppose She wants to stop:

u = 45 km/h = 45 x 1000m / 3600s = 12.5 m/s

a = - 5.8 m/s^2

t = 2s

distance needed to stop:

vf^2 - vi^2 = 2 a d

0^2 - 12.5^2 = 2(-5.8) d

d = 13.5 m

So it can stops within 28 m.

If she wants to cross:

for maximum acc. vf = 65 x 1000/3600 = 18.06 m/s

and vi = 12.5 m/s

18.06 = 12.5 + a(6)

a = 0.926 m/s^2

she had 2 sec.

lets see, how much distance she can cover.

d = ut + at^2 / 2

d = (12.5 x 2) + (0.926 x 2^2 /2 ) = 26.8 m

but if she want to cross within time then she have to cover 15+ 28 = 43 m.

which she can't.

so she must stop.