Question

basic formulae in motion chapter

Answer 1

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=ut+at22⇒s=ut+at22

⇒s=ut+12at2⇒s=ut+12at2 ----(iv)

The above equation is known as Second equation of motion.

Third Equation of Motion:

The third equation of motion is derived by substituting the value of time (t) from first equation of motion.

We know from first equation of motion, v=u+atv=u+at

⇒v−u=at⇒v-u=at

⇒at=v−u⇒at=v-u

⇒t=v−ua⇒t=v-ua -----(v)

We know that the second equation of motion is, s=ut+12at2s=ut+12at2

By substituting the value of tt from euqation (v) we get

s=u(v−ua)+12a(v−ua)2s=u(v-ua)+12a(v-ua)2

⇒s=u×v−ua+12a(v−u)2a2⇒s=u×v-ua+12a(v-u)2a2

⇒s=u(v−u)a+a×(v−u)22×a×a⇒s=u(v-u)a+a×(v-u)22×a×a

⇒s=uv−u2a+(v−u)22a⇒s=uv-u2a+(v-u)22a

⇒s=2(uv−u2)+(v−u)22a⇒s=2(uv-u2)+(v-u)22a

⇒2as=2uv−2u2+v2+u2−2uv⇒2as=2uv-2u2+v2+u2-2uv

⇒2as=−2u2+v2+u2⇒2as=-2u2+v2+u2

⇒2as=−u2+v2⇒2as=-u2+v2

⇒2as+u2=v2⇒2as+u2=v2

⇒v2=u2+2as⇒v2=u2+2as ---(vi)

This is called the Third equation of motion.

Answer 2

hi dear...
here is your answer.

• average velocity = initial velocity+ final velocity/2
Vav= u+v/2.
•average speed = Total distance travelled / total time taken.
•Vav = s/t
• Average velocity = displacement/ total time taken.
•acceleration = change in velocity/ time taken.
a=v-u/t
• v=s2-s1/t2-t1.
•v= u+ at
•s= ut + 1/2at ^2.
• 2as = v^2-u^2.

hope it helped you...