If she hits the brakes, how far will she travel before stopping?

[rakesh44]

Homework Statement

A person driving her car at 56 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). Should she try to stop, or should she make a run for it? The intersection is 15 m wide. Her car's maximum deceleration is -5.6 m/s2, whereas it can accelerate from 56 km/h to 70 km/h in 4.2 s. Ignore the length of her car and her reaction time. If she hits the brakes, how far will she travel before stopping?

Homework Equations

can someone at least give me a formula that i can use to find the answer??
thankss

 

[rl.bhat]

Refer any textbook and list the kinematic equations.

 

[tomcue]

The formula that can be used to find the distance traveled before stopping is:
d = (v^2-u^2)/2a
where d is the distance traveled, v is the final velocity, u is the initial velocity, and a is the acceleration.
In this case, the initial velocity (u) is 56 km/h, the final velocity (v) is 0 km/h (since the car will stop), and the acceleration (a) is -5.6 m/s2.
Therefore, using the formula above, the distance traveled before stopping can be calculated as:
d = (0^2-56^2)/2(-5.6)
d = 784 m
So, if the person hits the brakes, she will travel 784 m before stopping. This is much longer than the 30 m distance she is from the intersection, so it would be safer for her to stop rather than try to make it through the intersection before the light turns red.