**Derive the first equation of motion for uniformly accelerated rectilinear motion. OR Which equation of motion establishes the relationship between VF, vi, a, and t, driving the relationship between these quantities. OR Prove that if = vi + at. OR Derive the equation of motion which is independent of distance S?**

Difficulty: Easy

**Suppose a body is moving with initial velocity v _{i}, and after time t its velocity becomes v_{f}. Then acceleration a is given by**

a= $\frac{VF \: VI}{T}$

Or Vf - Vi = at

Vf = Vi + at

**Second Method (Graphical method):**

**The first equation of motion:**

** Speed-time graph for the motion of a body is shown in the figure. The slope of line AB gives the acceleration of a body.**

Slope of line AB= a= $\frac{AB}{AC}$ = $\frac{BD \: - \: CD}{OD}$

**As**

BD = V_{f}, CD = V_{i} and OD = t

**Hence, **a= $\frac{VF \: VI}{T}$

**Or, **V_{f} - V_{i }= at

V_{f} = V_{i }+ at

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