Solve Kinematics (3 in 1) Problems with Omid

[Omid]

Here there are 3 related problems which I need help with them :

37. Imagine that you are driving toward an intersection at a speed v_i just as the light changes from green to yellow. Assuming a response time of 0.6 s and an acceleration of -6.9 m/s^2, write an expression for the smallest distance (S_s) from the corner in which you could stop in time. How much is that if you are traveling 35 km/h?


I suggest this expression :
S_s= (v_i) (0.6 s) - [((v_i)^2) / 2a ]
And 12.67 as the numeric answer for the second part.

38. Considering the previous problem, it should be clear that the yellow light might reasonably be set for a time t_y, which is long enough for a car to traverse the distance equal to both S_s and the width of the intersection S_I.
Assuming a constant speed v_i equal to the legal limit, write an equation for t_y, which is independent of S_s.

I just don't get this one.

40. With problems 37 and 38 in mind, how long should the yellow light stay lit if we assume a driver response time of 0.6 s, an acceleration of -6.9 m/s^2, a speed of 35 km/h, and an intersection 25 m wide ? Which of the several contributing aspects requires the greatest time ?

I don't understand this one too.

Thanks
Omid

 

[HallsofIvy]

I suggest this expression :
S_s= (v_i) (0.6 s) - [((v_i)^2) / 2a ]
And 12.67 as the numeric answer for the second part.

You wrote "-" in the formula but clearly intended "+" (and used + to get 12.67)

38. You already have a formula for S_s. S_i is just some (given) fixed number. The distance you need to "traverse" as speed v_i is just the sum of those:
(v_i) (0.6 s) + [((v_i)^2) / 2a ] + S_i. What time is needed to go that distance at constant speed v_i ?

40. Now that you have finished 38 (what happened to 39?) just put the numbers you are given: v_i= 35, S_i= 25, etc. into the formula.

 

[Omid]

Yet there are 2 questions for me.
1. The formula for t_y ( problem 38 ) is not INDEPENDENT of S_s as the problem asks to be (our formula is : (v_i) (0.6 s) + [((v_i)^2) / 2a ] + S_i which is equivalently (v_i) (0.6 s) + [ S_s ] + S_i ).
2. Which of the several contributing aspects requires the greatest time ?
I think it's v_i, isn't it ?