Question

Derive the 2nd equation of motion?!

Answer 1

Avg velocity = (v+u)/2
=s/t
(v+u)/2=s/t
(u+at+u)/2=s/t
(2u+at)/2=s/t
2u/2 + at/2 = s/t
u+1/2 at= s/t
s=ut+1/2 at²

Answer 2

MOVEMENT OF THE OBJECT

An object is moving with uniform acceleration having initial velocity "u" and after time "t" second final velocity is "v". The distance travelled by an object is "s" in time "t" second. Below is the picture of graph according to movement of object.

DERIVATION OF SECOND EQUATION OF MOTION

Here,

Acceleration = Slope of the graph.

= (BD - CD)/AC

= BC /AC

where B is final velocity C is initial velocity and OD is time.

= (v - u)/t

Then acceleration is (v - u)/t  i.e.

=> a = (v - u)/t

=> v - u = at

=> v = u + at ........... (i)

Therefore, we have derived first equation of motion.

Now ,

Displacement = Area under graph.

= 1/2 OD (OA + BD)

= 1/2 t ( u + v)

Put value of v by using equation (i)

= 1/2 t ( u + u + at)

= 1/2 t (2u + at)

= ( 1/2t × 2u) + ( 1/2t × at)

= ut + 1/2at²

So,

s = ut + 1/2at².

Therefore second equation of motion derived.