Question

derive first equation of motion by using graph​

Answer 1

Answer:

Explanation:

Consider an object is moving with a uniform acceleration “a” along a straight line. Draw a line parallel to x-axis DA from point, D from where object starts moving. ... Draw another line BA from point B parallel to Y-axis which meets at E at y-axis.

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Answer 2

Consider the Velocity - Time graph of an object that moves under Uniform Acceleration as shown in the Figure Above.

From the graph,

We can see that Initial Velocity of the Object is u and then, it increases to v in time t. The Velocity changes at a Uniform Rate a.

It is also Clear that,

BC = BD + DC

BC = BD + OA

So we have, v = BD + u [Consider it Equation 1]

From the Velocity - Time graph, the Acceleration of the Object is given by -

$a = \frac{Change\:in\:Velocity}{Time\:Taken} = \frac{BD}{AD} \\\\a = \frac{BD}{OC} = \frac{BD}{t}$

which gives BD = at [Consider it Equation 2]

Putting Equation 2 in Equation 1, we get -

$v = u + at$ which is the Equation for Velocity - Time Relation.