Derivation of 1st Equation of Motion (Graphical Method)
Derivation of 1st Equation of Motion (Graphical Method)
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Q.: |
Derive
first equation of motion? |
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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. |
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