1. How is the duration of yellow traffic light decided?

Every signal in the state is owned, operated, and maintained by the municipality. The duration is based on a variety of factors, including vehicle speed, driver reaction time, braking time, and the grade of the road — whether it is uphill or downhill. Typically a yellow light can be between 3 to 6 seconds.

This problem is solved using the Institute of Transport Engineer (ITE) Yellow Change Interval Formula. This formula only works for the case where the driver approaches the intersection at the maximum allowable speed and not for turning drivers and drivers slowing down for obstacles since it yields several seconds too short. The time duration is rounded up to the nearest half second.
$$Y_{min} = {v_o t_p + {v_{o}^2 \over 2(a+G_g)} \over v_o}$$ where,
$Y_{min}$ = minimum yellow light duration
$v_o$ = initial velocity of the vehicle (speed limit)
$t_p$ = perception or reaction time constant
$v_ot_p$ = perception distance of driver
$a$ = safe comfortable deceleration of vehicle
$g$ = Earth's gravitational acceleration constant
$G$ = grade of the road in %/100 (downhill is -ve)
$a + G_g$ = effective deceleration of vehicle
${v_o \over a} + G_g$ = braking time of vehicle
${(v_o*{2 \over a} + G_g) \over 2}$ = braking distance of vehicle
$v_ot_p + {(v_o*{2 \over a} + G_g) \over 2}$ = critical distance $c$

Click here for derivation.

Traffic engineers define the critical distance $c$ as the distance the driver travels during the time that he perceives and reacts to the signal change to yellow plus the distance for him to brake to a stop.

$v_o$ is the initial velocity of the vehicle at the distance $c$ from the intersection. In the braking distance term, physics defines $v_o$ as the velocity of a vehicle where it is just beginning to brake to a stop. And in the world of transportation, $v_o$ must be at least the speed limit in order to give vehicles approaching the intersection the opportunity to stop.

These are the intents of the above formula when the light turns yellow:

  • If $v_o t_p > c \rightarrow$ driver must stop.
  • If $v_o t_p = c \rightarrow$ the driver arrives at the intersection the instant the light turns red.
  • If $v_o t_p < c \rightarrow$ driver does not have enough distance to stop. Hence, the driver must proceed before the light turns red.


  • It does not provide drivers the time to decelerate. Turning movements, cars pulling onto the road from side-streets, two close-by intersections, traffic congestion, hazards, railroad tracks, speed limit changes on the far side of the intersection, etc. are common circumstances where the driver must slow down.
  • The formula requires that drivers must act upon the exact position of the critical distance and the exact duration of the yellow light. Drivers have to estimate both distance and time and make an imprecise judgment.

2. What is the shelf life of water?

Water is extremely stable because of the covalent bond formed between Hydrogen and Oxygen. So, it is obvious that water as such has an indefinite shelf life. However, water at different temperatures does get adversely affected because of the type of containers it is stored in. Commercially available bottled water usually has a shelf life of two years.

Interestingly enough, tap/filtered water is very safe since it is highly monitored while the packaged water bottle usually use water from the municipal water supply and simply charge us for packaging. They doesn't use water from special water springs since it is rare and expensive.

Hot Temperatures

It is not recommended to store bottled water in hot environments like a garage or car. The high temperature often causes the BPA (bisphenol A, a polycarbonate plastic used in making containers to store food and beverages) plastic to slowly leach into the water. The US Food and Drug Administration considers small amounts of BPA safe, however high levels could possibly cause a health risk. Apart from this, warm conditions create comfortable grounds for the rise in the growth of bacteria and eventually spoils it.

Moderate Temperatures

Water left overnight or for a long period of time in an open glass or container is home to numerous bacteria and is not safe for drinking. A lot of dust, debris, and other small microscopic particles might have settled into the water. It is also observed that when water is left uncovered, carbon dioxide in the air starts to mix with it. This reduces the pH level of the water and gives it an off taste even though it might be safe.

Cold Temperatures

Storing water at cold temperature is not an issue. Even freezing and unfreezing is fine; the only thing to take into consideration is the volume of water being frozen and the type of container being used. Water expands in volume by eight percent on freezing, hence if it is a very low grade plastic, there are chances of it exploding in the freezer. Ideal is to freeze it in a good quality plastic bottle with some space for expansion or to use ice trays.

3. How does Vicks VapoRub work?

Decongestant tablets and nasal sprays may narrow blood vessels in our nose, leading to reduced swelling in our nasal passages. Vicks VapoRub however, isn't really a decongestant.

It is primarily made up of camphor, eucalyptus oil and menthol. When applied on our throat or chest, the strong vapors create a cooling sensation in our nasal passages that trigger receptors in our brain to feel that we are breathing more openly. Researchers say there is no science to back up the claim that Vicks makes it easier to breathe. Hence, it doesn't relieve a stuffed up nose or sinus congestion.

Vicks when used on our feet may soothe tired, achy feet since it may create a powerful cooling sensation that may temporarily override our ability to feel the pain. However, if it is applied to our feet for cold, it's unlikely the smell will be strong enough to reach our stuffy nose and make our brain believe it's breathing better.

Doctors recommend the best treatments for congestion are a bit of salt water, gentle rubber bulb suction, or warm drinks and, often, just letting the passage of time heal us.

From the desk of Vicks:

Q: How does Vicks VapoRub work?
A: Vicks VapoRub contains medicated vapors that enter the nose and mouth. The powerful long-lasting vapors start working in minutes to soothe coughs for easier breathing.

4. Why are all websites suddenly asking for cookies?

The pop-up alerts asking for cookies were largely triggered by two regulations in Europe: the General Data Protection Regulation (GDPR), enacted in the European Union in May 2018; and the ePrivacy Directive, first passed in 2002 and then updated in 2009.

The privacy law is designed to make sure users are aware of the data that companies collect about them, and to give them a chance to consent to sharing it. It requires companies to be transparent about what information they're gathering and why. And individuals get the right to access all their personal data, control access and use of it, and even have it deleted.

The most visible impact of this was the pop-up notification asking for consent to place a cookie (small text files that help websites identify returning users or track them across huge advertising networks) on our computer. Cookies themselves are not good or bad, it's how the website that places them on our computer uses them is concerning.

Since there aren't physical boundaries on the internet, it forced everyone around the world to comply with these new regulations regardless of where they may be located. The intent is to provide users with the details of what the website would do with the information they collected from us, which is why all of the notifications have a learn more link.

A button to reject the cookie may not be an option on some websites. Ignoring the notice, which is generally at the bottom of the screen will prevent the cookie from being placed on our computer, but that means the notice will be there whenever we go on that site. Websites that don't ask if we are OK with sharing cookies are still taking it without being transparent about it.

Using the private or incognito browsing option will automatically get rid of any cookies placed on our computer. The flip-side of this is that some companies simply won't let us use their website if we don't accept a cookie. But for the most part, we'll still be able to access the majority of the internet without accepting cookies.

5. How does our body get vitamin D from sunlight?

When our skin is exposed to sunlight, the ultraviolet B (UVB) rays interact with a protein called 7-Dehydrocholesterol (7-DHC) in the skin, converting it into previtamin D3, the inactive form of vitamin D. Through a process called hydroxylation (carbon-hydrogen bond is oxidized into carbon-hydroxyl bond), the liver and kidneys turn the stored previtamin D into the active form called calcitriol (vitamin D3).

Several factors affect how much vitamin D a person's body can make from exposure to the sun, such as season, time of day, geographical location, skin color, air quality, latitude, altitude, weight, age, and use of sunscreen.


It is important to note that the UVB rays cannot penetrate through windows. So people who work next to sunny windows are still prone to vitamin D deficiency.

Skin Color

Since darker-skinned people have more melanin (a compound that protects against skin damage by reducing the amount of UVB light absorbed), they need more time in sunlight to make the same amount of vitamin D than lighter-skinned people.


An SPF 15 sunscreen filters out 93 percent of UVB rays, SPF 30 keeps out 97 percent, and SPF 50 filters out 98 percent. This leaves anywhere from 2 to 7 percent of solar UVB reaching our skin. Studies have never found that everyday sunscreen use leads to vitamin D insufficiency, rather the opposite.

10 to 15 minutes of exposure to arms, legs, abdomen and back, two to three times a week with good sun protection produces all the vitamin D our body can muster. After that, our body automatically starts to dispose of vitamin D to avoid an overload and the sunlight then starts doing us more harm than good. In general, the longer we stay in the sun without protection, the greater our risk of skin cancer.


  1. Traffic light: The minimum yellow light change interval is obtained by dividing the critical distance from the traffic light by the initial vehicle velocity. Cities usually follow this formula and keep the duration between 3 to 6 seconds.
  2. Water: Water doesn't expire, but bottled water does either because the plastic can leach into water or due to bacteria growth.
  3. Vicks: Vicks is a Placebo!
  4. Cookies: The European Union General Data Protection Regulation enacted the privacy law to make sure users are aware of the data that companies collect about them, and to give them a chance to consent to sharing it.
  5. Vitamin D: The ultraviolet B rays interact with a protein called 7-Dehydrocholesterol in the skin, converting it into previtamin D3. Through hydroxylation, the liver and kidneys then turn it into vitamin D3.

© Copyright 2023  |  Dipam Patel