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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