Question

# Derive following equations for a uniformly accelerated motion : (i) v=u+at (ii) S=ut+12at2 (iii)  v2=u2+2aS where the symbols have their usual meanings.

Solution

## (1) First equation of Motion: V = u + at soln. Consider a body of mass “m” having initial velocity “u”.Let after time “t” its final velocity becomes “v” due to uniform acceleration “a”. Now we know that: Acceleration = change in velocity/Time taken => Acceleration = Final velocity-Initial velocity / time taken => a = (v-u) /t =>at = v-u =>v = u + at This is the first equation of motion. —————————————- (2) Second equation of motion: sol. Let the distance travelled by the body be “s”. We know that Distance = Average velocity X Time Also, Average velocity = (u+v)/2 .: Distance (t) = …….eq.(1) Again we know that: v = u + at substituting this value of “v” in eq.(1), we get This is the 2nd equation of motion. …………………………………………………………… (3) Third equation of Motion sol. We know that V = u + at => v-u = at or t = (v-u)/a ………..eq.(2) Also we know that Distance = average velocity X Time . This is the third equation of motion

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