Question

derive the three equation of motion​

Answer 1

Answer:

The three equations are,

• v = u + at
• v = u + atv² = u² + 2as
• s = ut + ½at²

where, s = displacement; u = initial velocity; v = final velocity; a = acceleration; t = time

First equation :

Aasume a body that has a mass “m” and 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

Therefore, Acceleration = (Final Velocity-Initial Velocity) / Time Taken

Hence, a = v-u /t or at = v-u

Therefore, we have: v = u + at

Second equation :

We have, v = u + at. Hence, we can write

t = (v-u)/a

Also, we know that,

Distance = average velocity × Time

Therefore, for constant acceleration we can write:

Average velocity= (final velocity +initial velocity)/2

= (v+u)/2

Hence, Distance (s) = [(v+u)/2] × [(v-u)/a]

or s = (v² – u²)/2a

or 2as = v² – u²

or v² = u² + 2as

Third equation:

Let the distance be “s”. We know that

Distance = Average velocity × Time. Also, Average velocity = (u+v)/2

Therefore, Distance (s) = (u+v)/2 × t

Also, from v = u + at, we have:

s = (u+u+at)/2 × t = (2u+at)/2 × t

s = (2ut+at²)/2 = 2ut/2 + at²/2

or s = ut +½ at²

HOPE IT HELPS..

Answer 2

Answer:

hope it helps u

Step-by-step explanation:

First Equation of Motion:

The final velocity (v) of a moving object with uniform acceleration (a) after time, t.

Let, the initial velocity = u.

Final velocity = v.

Time = t

Acceleration = a

We know that, Acceleration (a) =Change in velocityTime taken=Change in velocityTime taken

⇒a=Final velocity-Initial velocityTime taken⇒a=Final velocity-Initial velocityTime taken

⇒a=v−ut⇒a=v-ut

⇒at=v−u⇒at=v-u

⇒at−v=−u⇒at-v=-u

⇒−v=−u−at⇒-v=-u-at

⇒v=u+at⇒v=u+at ---(i)

This equation is known as first equation of motion.

Second Equation of Motion:

Distance covered in time (t) by a moving body.

Let, Initial velocity of the object = u

Final velocity of the object = v

Acceleration = a

Time = t

Distance covered in given time = s

We know that,

Average velocity =Initial velocity+Final velocity2=Initial velocity+Final velocity2

∴ Average velocity =u+v2=u+v2 ----(ii)

We know that, Distance covered (s) in given time = Average velocity x Time

Or, s = Average velocity x Time -----------------(iii)

After substituting the value of average velocity from equation (ii) we get

⇒s=u+v2×t⇒s=u+v2×t

After substituting the value of ‘v’ from first equation of motion we get,

⇒s=u+(u+at)2×t⇒s=u+(u+at)2×t

⇒s=u+u+at2×t⇒s=u+u+at2×t

⇒s=2u+at2×t⇒s=2u+at2×t

⇒s=2ut+at22⇒s=2ut+at22

⇒s=2ut2+at22⇒s=2ut2+at22

⇒s=u