Time (t)
t=s/v
Distance (s) Speed (v) acceleration
(a)
s=vt v=s/t a=v/t
A Grand Prix motorcycle circles the track. After
level pegging for most of the race, its average lap time is compared
with the other competitors and found to be 0.2 seconds quicker than
the next fastest. With a top speed recorded on the longest straight
of 100 metres per second (m/s)
- that's over 200mph -
it's right up there with the best, but it's still not primo
top-speed. But the bike is winning – so, it must be going quicker
through the bends. If it carries on like this, by the time the race
finishes in five laps time, the motorcycle will have won by a margin
of one second. It covers the final lap in 50 seconds, winning with
an average speed of 50m/s (during
this lap). This means that the track is 2500 metres in
length. As the machine in second place is 0.2 seconds slower over
this distance, its average speed, therefore, is 49.98m/s.
Prediction, calculation and evaluation; all possible because of
time.
Time: the only proper constant in the world we
understand. While everything we can see and touch can vary, time is
the truly independent ingredient. Time gives the fixed marker posts
of change; a uniform grid over which all that happens in life is
laid. Unlike anything else in our everyday perception of the world,
it never varies. Everything you can physically see changes at
differing rates, because of time, and are only quantifiable because
time is unvarying and constant. Time is both the base and the
dimension that provides the measure of life. Without time there would
be no comparison of events – change would be unquantifiable and
unpredictable. Our deterministic world could not function without
the concept of time.
Time is sometimes referred to as the fourth
dimension because to find meaning in the words, faster, slower,
quicker, a perceptible but intangible benchmark is required, one that
exists outside the world we see. Imagine you have no recognition of
time. A truck overtakes you on the motorway, he's in front of you,
so he will arrive before you. How do you arrive first? Your truck
must get in front of his, but how do you get the front of your truck
ahead? The simple answer is to increase speed. But time doesn't
exist, so neither does speed.
When speed increases or decreases, it simply means
the distance travelled changes in a fixed period of time. When we
accelerate or decelerate, the distance travelled in a fixed period of
time changes in a fixed period of time. Using the standard (SI)
units of time and space, metres and seconds, a truck travelling at a
speed of 13m/s, travels 13
metres every second. If it accelerates at a rate of 2 metres per
second, per second (m/s/s),
its speed will increase by 2 metres per second every second. So, if
a truck travelling at 13 m/s accelerates at a rate of 2 m/s/s,
after 1 second it will be travelling at 15 m/s,
after 2 seconds, its speed will have increased to 17 m/s.
Time permits change in the physical world; speed,
acceleration and interest on savings are all changes in things we can
touch. Time makes change relative. When you next overtake another
truck on the motorway, think about it. A 16.5 metre artic attempts
to pass another. The distance needed from the front of the
overtaking vehicle passing the rear of the other, to its rear passing
the front of the other, is 33 metres. This is an absolute minimum and
takes no account of the extra distance required to turn back to the
lane in front of the overtaken truck. You are averaging 56mph,
he's averaging 55mph. The
difference is about 0.5m/s.
The time needed is 66 seconds,
just over a minute. In that time you will have travelled over 1650
metres, a little more than a mile.
So, by overtaking,
you gain just over 30 metres for every mile
travelled, and it takes about a minute. At 56mph, a 200 mile journey
will take 3 hours 34 minutes. Or, 3 hours and 38 minutes had you sat
behind the other lorry. Four minutes: a motorcycle on an A road
would cover 4 miles – at 60mph; a mile a minute. Roger Bannister
could change position by a mile. A Grand Prix motorcycle, travelling
at over 200mph would
have overtaken your truck in just under a second. (As the comparison
is between your truck and the motorcycle, the relative change in
distance is 16.5 metres, plus 2 metres for the length of the bike.)
And, at 200mph, the race bike would arrive at the end of the 200 mile
journey no less than two and a half hours before your truck (had you
both started in the same place and, of course, at the same time).
That's enough time for a serious athlete to run a marathon. It's all
a matter of time.
