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Grade 12th passMechanics

A PARTICLE MOVES ALONG A STRAIGHT LINE WITH UNIFORM ACCELERATION. IF P1 AND P2 ARE LINEAR MOMENTA WHILE CROSSING THE POINTS A AND B, WHAT IS MOMENTAUM WHILE CROSSING C WHICH IS THE MID POINT OF A AND ?????.....

can u give me proof sir

AKOJU SAI KUMAR

8 Years agoGrade 12th pass

1 Answer

Shailendra Kumar Sharma

8 Years ago

Uniform acceleration, let say the acceleration be a, and a will be constant.
Now dv/dt =a
assume he mass of object m and at point A assume the velocity be v1 and at the point B to velcity be v2
Now distance between A and B can be calculated by
v2=u2+2as
so v₂² =v₁² + 2aS
so the distance between A and B will be S=(v₂² – v₁²)/(2a)

at the midpoint, the distance will be S/2 so C is s/2 far from A
so velocity at C

v_c² =v₁² + 2aS = v₁² + 2a{(v₂² – v₁²)/(2a)}(/2)
=v₁² +(v₂² – v₁²)/2=(v₂² + v₁²)/2

So v_c² = (v₂² + v₁²)/2 multiple by m² both side

m² v_c² = m² (v₂² + v₁²)/2

P_c² = (P_A² +P_B²)/2

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