Question

A partide moves along a straight line AB with constant acceleration. Its velocities are u and at A and B respectively. Show that its velocity at the mid-point of AB is under root u square + v square/2​

Answer 1

Answer:

Answer

Let the distance between A and B=s and as mentioned C is the midpoint of A and B thus distance between A C and

C B=2s​

From equation of motion we get distance between AB

v2=u2+2as

s=2av2−u2​----------(1)

Let speed of the vehicle be pm/s at point C

Again from equation of motion we get,

p2=u2+2a2s​

as distance between A and C is 2s​

s=ap2−u2​-------(2)

computing 1 and 2 we get

ap2−u2​=2av2−u2​

p2=2v2+u2​p=2v2+u2​

​

Explanation:

Answer 2

Explanation:

Let the total distance be ( s ) .

let the points be A , B and midpoint = C

• velocity at point A = v1

• velocity at point B = v2

Let Velocity at point C ( midpoint ) = x .

Between A and B :-

=> v2^2 = v1^2 + 2as

=> v2^2 - v1^2 = 2as

=> as = (v2^2 - v1^2) / 2

Between A and C :-

=> x^2 = v1^2 + 2as/2 ( s = s/2 as midpoint ) .

=> x^2 = v1^2 + as

putting value of ' as ' in this equation.

=> x^2 = v1^2 + ( v2^2 - v1^2 ) / 2

=> x^2 = ( v1^2 + v2^2 ) / 2

→ x ( velocity at midpoint of AB ) =>

under root v^2 + u^2 upon 2

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