Derivation of 1st Equation of Motion (Graphical Method)

Q.:

Derive first equation of motion?

Ans.

Consider a body moving with initial velocity vi in a straight line with uniform acceleration a. Its velocity becomes vf after time t. The motion of body is described by speed-time graph as shown in the figure below Slope of line AB gives the acceleration ‘a’ of a body. $$slope of line\overline{AB}=a=\frac{\overline{BC}}{\overline{AC}}=\frac{\overline{BD}-\overline{CD}}{OD}$$ As $$\overline{BD}=v_{f}$$ $$\overline{CD}=v_{i}$$ $$\overline{OD}=t$$ Putting these values in the above equation we get $$a=\frac{v_{f}-v_{i}}{t}$$ $$v_{f}-v_{i}=at$$ $$v_{f}=v_{i}+at$$ This is the 1st equation of motion.