using velocity time graphfor uniform acceleration, establish velocity time relation
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Answer:
Let an object is moving with uniform acceleration.
Let an object is moving with uniform acceleration.
Let the initial velocity of the object = u
Let the object is moving with uniform acceleration, a.
Let object reaches at point B after time, t and its final velocity becomes, v
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.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.