Question

Derive the equation for velocity-time relation (v=u+at) by graphical method​

Answer 1

Answer:

$\textsf{The acceleration of the body=slop of v-t graph}$

$\textsf{i.e.}$

$a= \frac{BC}{AC}= \frac{BD-CD}{OD}= \frac{v-u}{t}$

$\implies v-u=at$

$i.e. \: \: \: \: \: v=u+at$

$\textsf{where t-time taken, u initial velocity,v-final velocity and acceleration}$

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Answer 2

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Let OE = time, t Now, from the graph, BE = AB + AE ⇒ v = DC + OD (Since, AB = DC and AE = OD) ⇒ v = DC + u (Since, OD = u) ⇒ v = DC + u -------------------

(i) Now, Acceleration (a) =(Change in velocity)/(Time taken) a= v – ut ⇒ a = v - ut ⇒ a= OC – OD t = DC t ⇒a = OC-OD t =DC t ⇒at=DC ⇒at=DC -----

(ii) By substituting the value of DC from (ii) in (i) we get v= at + u v = at + u ⇒ v = u + at ⇒ v = u + at Above equation is the relation among initial velocity (u), final velocity (v), acceleration (a) and time (t). It is called first equation of motion.

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