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3 equation of motion

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Ashwani96

The document discusses three equations of motion: 1) The first equation is v=u + at, which gives the velocity acquired by an object with initial velocity u that experiences a uniform acceleration a over time t. 2) The second equation is s=ut + 1/2at^2, which gives the distance traveled by an object with initial velocity u and uniform acceleration a over time t. 3) The third equation is v=u + 2as, which can be derived by eliminating time t from the first two equations and gives the final velocity of an object that travels a distance s with initial velocity u and uniform acceleration a.

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THREE EQUATION’S OF MOTION NAME :- ASHWANI KUMAR SUBJECT:-PHYSICS PROJECT(EQUATION OF MOTION)
•First Equation of Motion The first equation of motion is v=u + at. It gives the velocity acquired by a body in time t. Consider a body having initial velocity ‘u’. Suppose it is subjected to a uniform acceleration ‘a’ so that after time ‘t’ its final velocity becomes ‘v’. Now, from the definition of acceleration we know that; —> Acceleration=Change in velocity Time taken —> Acceleration=Final velocity –Initial velocity Time taken —> a=v - u t —> at=v - u —> v=u + at
•Second Equation of Motion The second equation of motion is s=ut + 1at. It gives 2 the distance traveled by a body in time t. Consider a body having initial velocity ‘u’ and a uniform acceleration ‘a’ for time ‘t’ so that its final velocity becomes ‘v’. .Let the distance traveled by the body in this time ‘s’. The distance travelled by a moving body in time ‘t’ can be found out by considering its average velocity. Since the initial velocity of the body is ‘u’ and its final; velocity is ‘v’ ,the average velocity is given by: —> Average velocity=Initial velocity+ final velocity 2 —> Average velocity=u + v 2
Distance travelled= average velocity x Time —> S=(u + v) x t …………………….(1) 2 From the first equation of motion we have ,v=u + at. Putting the value of v in equation (1), we get —> S=(u+ u+ at) x t 2 —> S=(2u+at) x t 2 —> S=2ut+ at2 2 —> S= ut+1at2 2
•Third Equation of Motion The third equation of motion is v=u+2as. It gives the velocity acquired by a body in traveling a distance ‘s’ Consider a body having initial velocity ‘u’ and a uniform acceleration ‘a’ for time ‘t’ so that its final velocity becomes ‘v’. .Let the distance traveled by the body in this time ‘s’. The distance travelled by a moving body in time ‘t’ can be found out by considering its average velocity. Since the initial velocity of the body is ‘u’ and its final; velocity is ‘v’ ,the average velocity is given by: The third equation of motion can be obtained by eliminating t between the first two equation of motion. From second equation of motion we have; S=ut+1at 2 ……………..(1)
And from the first equation of motion we have; —> v=u + at This can be rearranged and written as —> at=v - u —> t=v - u a Putting the value of tin equation (1)we get; —> S=u (v-a)+1a(v-u/a) 2 —> S=uv-u+a(v+u-2uv) a 2a —> S=2uv-2u+v+u-2uv 2a —> 2as= v – u —> V=u+2as
THE END

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3 equation of motion

  • 1. THREE EQUATION’S OF MOTION NAME :- ASHWANI KUMAR SUBJECT:-PHYSICS PROJECT(EQUATION OF MOTION)
  • 2. •First Equation of Motion The first equation of motion is v=u + at. It gives the velocity acquired by a body in time t. Consider a body having initial velocity ‘u’. Suppose it is subjected to a uniform acceleration ‘a’ so that after time ‘t’ its final velocity becomes ‘v’. Now, from the definition of acceleration we know that; —> Acceleration=Change in velocity Time taken —> Acceleration=Final velocity –Initial velocity Time taken —> a=v - u t —> at=v - u —> v=u + at
  • 3. •Second Equation of Motion The second equation of motion is s=ut + 1at. It gives 2 the distance traveled by a body in time t. Consider a body having initial velocity ‘u’ and a uniform acceleration ‘a’ for time ‘t’ so that its final velocity becomes ‘v’. .Let the distance traveled by the body in this time ‘s’. The distance travelled by a moving body in time ‘t’ can be found out by considering its average velocity. Since the initial velocity of the body is ‘u’ and its final; velocity is ‘v’ ,the average velocity is given by: —> Average velocity=Initial velocity+ final velocity 2 —> Average velocity=u + v 2
  • 4. Distance travelled= average velocity x Time —> S=(u + v) x t …………………….(1) 2 From the first equation of motion we have ,v=u + at. Putting the value of v in equation (1), we get —> S=(u+ u+ at) x t 2 —> S=(2u+at) x t 2 —> S=2ut+ at2 2 —> S= ut+1at2 2
  • 5. •Third Equation of Motion The third equation of motion is v=u+2as. It gives the velocity acquired by a body in traveling a distance ‘s’ Consider a body having initial velocity ‘u’ and a uniform acceleration ‘a’ for time ‘t’ so that its final velocity becomes ‘v’. .Let the distance traveled by the body in this time ‘s’. The distance travelled by a moving body in time ‘t’ can be found out by considering its average velocity. Since the initial velocity of the body is ‘u’ and its final; velocity is ‘v’ ,the average velocity is given by: The third equation of motion can be obtained by eliminating t between the first two equation of motion. From second equation of motion we have; S=ut+1at 2 ……………..(1)
  • 6. And from the first equation of motion we have; —> v=u + at This can be rearranged and written as —> at=v - u —> t=v - u a Putting the value of tin equation (1)we get; —> S=u (v-a)+1a(v-u/a) 2 —> S=uv-u+a(v+u-2uv) a 2a —> S=2uv-2u+v+u-2uv 2a —> 2as= v – u —> V=u+2as