write three equation of motion?
Answers
Hence, these equations are used to derive the components like displacement(s), velocity (initial and final), time(t) and acceleration(a). Therefore they can only be applied when acceleration is constant and motion is a straight line.
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The three equations are,
v = u + at.
v² = u² + 2as.
s = ut + ½at²
Answer:
Three equations of motion are -
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.
9 Science
Motion
Equation of Motion:
Relation among velocity, distance, time and acceleration is called equations of motion. There are three equations of motion:
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+