It`s Time

Why is it that a person, who would never dream of stepping into the path of a 44 tonne truck travelling at 90kph, drives one in fog at a similar speed? Sitting behind that wafer thin sheet of glass and metal waiting for the rear of a semi-trailer to appear out of nowhere – from normal day to death in just a few seconds.

A truck travelling at 90kph (56mph) is doing 25 metres (that`s 82 feet or 27 yards) every second.  Drivers, it is estimated, will have typical reaction times of between 0.6 seconds to 1.5 seconds.  The shorter time is considered pretty fast, an alert driver prepared for something to occur, maybe, so slower times within the range are often more common, although this will depend on a number of factors. Times greater than 1.5 seconds may also occur as a characteristic of some driving conditions, motorway driving, for example, which tends to be monotonous. (Interestingly, The Highway Code relies on a time of about 0.7 seconds for its `typical` stopping distances.)  At 56mph, times of 0.6 to 1.5 seconds represent distances travelled of between 15 metres and 38 metres (49 – 125 feet) as the driver reacts.  These are the distances the truck covers before any brakes are applied.  So, step out 125 feet in front of a driver with a 1.5 second reaction time and the front of his truck will strike you at 56 mph.  The same driver, travelling in fog where visibility is restricted to 125 feet would hit a stationary vehicle at a similar speed – and at exactly the same time his foot buried the brake pedal. 

Of course stopping completely takes longer.  If a truck under heavy braking achieved a deceleration of 0.7g, it would slow at a rate of about 7 metres per second (16mph) every second.  For our driver, stopping from a speed of 90kph, it would take 1.5 seconds of reaction plus the time for the vehicle to brake to standstill.  At a deceleration rate of 7 metres per second, per second, this would mean a total time of about 5 seconds.  In distance that`s 125 feet of reaction plus about 150 feet of braking.  A total of 275 feet (92 yards or 83 metres) to stop from 56mph (90kph) – or 5 artic truck lengths.

Why does a driver travelling 1 kph faster than the truck in front attempt to overtake it, when it takes several kilometres to do so, and such a manoeuvre often has little effect on the total journey time? The same driver wouldn`t think twice about spending 15 minutes idly chatting before going home at the end of the day.

In terms of time, a truck travelling at 1kph (about 0.3 metres per second, or just under 1mph) faster than the vehicle in front will take whatever `relative` distance it needs to pass it, divided by this `relative` speed difference.  The absolute minimum relative distance for the overtaking vehicle is from when its front passes the rear of the other vehicle, to when its rear passes the front of the other vehicle.  Assuming that both vehicles are artics, that`s a relative distance of about 33 metres, which, at 1kph, takes 1 minute and 50 seconds. At 90 kph that`s an absolute distance of just over 1 mile (just under 3 km).

On a journey of 124 miles (200km), a 1 kph difference represents a time difference of 4 minutes.  That`s 8 minutes if the difference is 2kph, or the journey is about 250 miles.

Why do drivers race towards red or amber traffic lights, braking sharply before coming to a halt, when, subsequently, every second they have to wait seems to last a lifetime.

If a traffic light phase, including amber and red and amber phases, lasts, say, 30 seconds, then the less time spent sitting waiting the less frustrating it seems.  Braking at a harsh rate of 0.7g, or 16mph every second, would mean coming to a halt from 56 mph (90kph) in 3.5 seconds, from 48 mph in 3 seconds and from 32 mph in 2 seconds.  But, by easing off and slowing at a much lower rate, an average of 0.2g, for example, which is about 4mph every second, would take 4 times as long as those times shown for 0.7g.  So, 8 seconds from 30 mph, that`s 6 seconds less of sitting, waiting time.

Of course it all depends on the distance available, how far the truck is from the lights when they change, but how often do you see vehicles, all types of vehicle, bowling towards lights that are changing to red.  They could ease off, relax, themselves and their vehicle, and take some time.

Why is it that when we are busy, time passes quickly, but when we are waiting, time passes slowly?

When a vehicle brakes hard, harsh enough to activate its ABS, the deceleration rate can be considered constant. At 0.7g, the vehicle will slow by 16mph every second.  Under these conditions speed and time have a linear relationship – one is directly proportionate to the other.  Work, the energy of a system, on the other hand, is not directly proportionate to either time or speed.  To do more work takes longer, so that speed loss at higher speeds needs greater distance.  To slow at 0.7g from 50 mph to 40 mph takes in the region of 12 metres. But from 20 mph to 10 mph it takes only something close to 4.5 metres.

Could it be the more we work, the more time passes? In our world, a world that seldom exceeds 90kph, time is constant and finite. Each second is the same as the next and time travels in one direction.  Time is not to be wasted by working unnecessarily. It`s time to slow down; It`s time to relax.  It`s time to appreciate time.