Question

write three equation of motion and derived them

Answer 1

Answer:

The three equations of motion are:

(1) $v=u+at$

(2) $s=ut+\frac{1}{2} at^{2}$

(3) $v^{2} =u^{2} +2as$

Derivaion:

Let a body is moving in a straight line with uniform acceleration. Let its initial velocity be u and acceleration a. If velocity after time t is v and displacement is s then

Derivation of first equation of motion

acceleration is nothing but rate of change of velocity

Thus, acceleration = (final velocity - initial velocity) ÷ Time

∴ $a=\frac{v-u}{t}$

⇒ $at=v-u$

⇒ $v=u+at$

Derivation of second equation of motion

Displacement = Average velocity × time

∴ $s=(\frac{v+u}{2}) t$

⇒ $s=(\frac{u+at+u}{2} )t$    (∵ v = u+at)

⇒ $s=\frac{2ut+at^{2}}{2}$

⇒ $s=ut+\frac{1}{2}at^{2}$

Derivation of third equation of motion

Displacement = Average velocity × time

∴ $s=(\frac{v+u}{2}) t$

⇒ $s=(\frac{v+u}{2} )(\frac{v-u}{a} )$              (∵ $t=\frac{v-u}{a}$)

⇒ $s=\frac{v^{2}-u^{2} }{2a}$

⇒ $2as=v^{2} -u^{2}$

⇒ $v^{2} =u^{2} +2as$

Answer 2

Explanation:

The three equations of motion are:

(1) v=u+atv=u+at

(2) s=ut+\frac{1}{2} at^{2}s=ut+

2

1

at

2

(3) v^{2} =u^{2} +2asv

2

=u

2

+2as

Derivaion:

Let a body is moving in a straight line with uniform acceleration. Let its initial velocity be u and acceleration a. If velocity after time t is v and displacement is s then

Derivation of first equation of motion

acceleration is nothing but rate of change of velocity

Thus, acceleration = (final velocity - initial velocity) ÷ Time

∴ a=\frac{v-u}{t}a=

t

v−u

⇒ at=v-uat=v−u

⇒ v=u+atv=u+at

Derivation of second equation of motion

Displacement = Average velocity × time

∴ s=(\frac{v+u}{2}) ts=(

2

v+u

)t

⇒ s=(\frac{u+at+u}{2} )ts=(

2

u+at+u

)t (∵ v = u+at)

⇒ s=\frac{2ut+at^{2}}{2}s=

2

2ut+at

2

⇒ s=ut+\frac{1}{2}at^{2}s=ut+

2

1

at

2

Derivation of third equation of motion

Displacement = Average velocity × time

∴ s=(\frac{v+u}{2}) ts=(

2

v+u

)t

⇒ s=(\frac{v+u}{2} )(\frac{v-u}{a} )s=(

2

v+u

)(

a

v−u

) (∵ t=\frac{v-u}{a}t=

a

v−u

)

⇒ s=\frac{v^{2}-u^{2} }{2a}s=

2a

v

2

−u

2

⇒ 2as=v^{2} -u^{2}2as=v

2

−u

2

⇒ v^{2} =u^{2} +2asv

2

=u

2

+2as