Some Basics of Distance -time graph!!!

Distance-Time Graph is a graph where Y-axis represents distance traveled and X-axis represents time....
What we can determine from Distance-time graph?
1. We can determine the velocity( whether it is increasing or decreasing at a given moment)...
2. We can determine the Displacement...
3.We can determine the time taken to cover a given distance and so on.........

//Let us Discuss very important part of Distance-time graph//

How to determine from a distance- time, that whether the velocity related to distance time curve is increasing or decreasing ?

For all this stuff you need to clear two of the very important concepts...

1.Tangent function is an increasing function in the interval [- 1.57,1.57] => [0,1.57], a tangent function is nothing but tan@
(where @ is nothing but the angle in degrees), this usually we all study in the basic trigonometry in our junior classes
but to know a bit more about tangent function visit www.indiantan.com......

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For your simplicity let me explain it to you in a simpler way all of you ,i suppose know that tan0=0 ,tan30=(1/3)^1/2
and tan45=1 ,and tan60=(3)^1/2, tan90=infinite... from all this you all can easily determine that as 90>60>45>30>0
tan90>tan60>tan45>tan30>tan0.. it implies tan@ is an increasing function....

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2. A concave up curve is a curve shaped like a bowl whose hole is in the upward direction and Concave down is similarly
a curve whose hole is pointing in the downward direction........

Now how to determine whether the velocity is increasing or decreasing from the given Distance-time curve....

Consider the two curve shown (a) is a concave upward curve and(b) is a concave downward curve , now consider the
angles shown in the graph(a) as you can determine from the graph that angle a < b < c therefore tana< tanb < tanc ...
now you need to know that dx/dt that is ( ratio of differential change in distance to the differential change in time)..is nothing but
the tangent drawn to the curve at that point and that in turn is nothing but the velocity at that point ,so as the tangent function is
increasing therefore velocity is increasing ,similarly in the graph(b) the tangent function is decreasing and henceforth the velocity
is decreasing.....

So one thing you need to REMEMBER BY HEART is that a concave upward curve in a distance-time graph represents the INCREASING
VELOCITY and concave downward represents the DECREASING VELOCITY....

Also from the graph(a) determine that at a point p velocity is nothing but the tangent at that point..to know more about tangent to a curve visit
www.tangentcurve.com

With regards!!!

Wishing you success for your exams...
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Posted in: basics,physics