Derivation of First Equation of Motion
Derivation of First Equation of Motion
Derivation of First Equation of Motion:
Equation for Velocity-Time Relation (First Equation)
Velocoty time graph of an object that moves under uniform acceleration is shown in figure. Let the initial velocity of the object be u (at point A) and then it increases to v (at point B) in time t. The velocity changes at a uniform rate a.
The perpendicular lines BD and BE are drawn from point B on the time and the velocity axIs respectively, the initial velocity is represented by OA, the final velocity is representeed by OE and the time interval t. Let us draw AC parallel to OD.. From the graph, we observe that BD= BC + CD = BC + OA ...(i) But BD = v and OA = u and substituting in Eq. (i) we get v = BC + u or BC = v -u From the velocity-time graph, the acceleration of the object is given by the slope |  |
Substituting OD= t, we get
or BC = at
Using Eqs. (ii) and (iii), we get
v = u + at
Hence, the first equation of motion has been derived.
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