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எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்

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Subjects
Science State Board
Class 9
Motion
Textbook questions

11. Answer in detail - I

Exercise condition:

7 m.

1. Derive equations of motion by graphical method.

Solution:

An object is in motion with

$initial\ velocity\ u$ attains a

$final\ velocity\ v$ in

$time\ t$ due to

$acceleration\ a$ , with

$displacement\ S$ .

Let us try to derive these equations by graphical method.

Equations of motion from velocity – time graph:

From the above graph, we can observe that the velocity changes with time for a uniformly accelerated object.

The object starts from the point

$D$ in the graph with velocity

$u$ . The velocity of an object keeps increasing, and after time

$(t)$ , it reaches the point

$B$ on the graph.

Therefore,

The initial velocity of the object,

$u\ =\ DA\ =\ CB$
$u\ =\ OD\ =\ EA$
$u\ =\ DC\ =\ AB$
$u\ =\ OE\ =\ DA$

Then, the final velocity of an object,

$v\ =\ OD\ =\ EA$
$v\ =\ DA\ =\ CB$
$v\ =\ DC\ =\ AB$
$v\ =\ OC\ =\ EB$

Time,

$t\ =\ OE\ =\ DA$
$t\ =\ OD\ =\ EA$
$t\ =\ DC\ =\ AB$
$t\ =\ OC\ =\ EB$

From the graph, we can also find that

$AB\ =\ DC$

i) First equation of motion:

We already knew that acceleration,

$acceleration\ (a)\ =\ \frac{Change\ in\ displacement}{time}$
$acceleration\ (a)\ =\ \frac{Change\ in\ distance}{time}$
$acceleration\ (a)\ =\ \frac{Change\ in\ velocity}{time}$

Substitute the values and simplifying,

First equation of motion,

$i = i + i i$

Second equation of motion,

$i = i i + \frac{i}{i} \times (i i^{i})$

Third equation of motion,

$i^{i} = i^{i} + i i i$

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