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Explanation:
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Answer:
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.The body has an initial velocity u at a point A and then its velocity changes at a uniform rate from A to B in time t. In other words, there is a uniform acceleration a from A to B, and after time t its final velocity becomes v which is equal to BC in the graph. The time t is represented by OC.
To complete the figure, we draw the perpendicular CB from point C, and draw AD parallel to OC. BE is the perpendicular from point B to OE.
Now, Initial velocity of the body, u=OA ...(1)
And, Final velocity of the body, v=BC ...(2)
But from the graph BC=BD+DC
Therefore, v=BD+DC ...(3)
Again DC=OA
So, v=BD+OA
Now, from equation (1), OA=u
So, v=BD+u ...(4)
We should find out the value of BD now. We know the slope of a velocity-time graph is equal to the acceleration, a.
Thus, Acceleration, a= slope of line AB
or a= BD
AD
But AD=OC=t, so putting t in place of AD in the above relation, we get:
a= BD
t
or BD=at
Now, putting this value of BD in equation(4), we get:
v=u+at