Question

A point moves with uniform acceleration $v_1,v_2$ and $v_3$ denote the average velocities in three successive intervals of time $t_1, t_2$ and $ t_3 $. Correct relation among the following is

• A. $(v_1 -v_2 ):(v_2 -v_3 ) = ( t_1 -t_2) : (t_2 -t_3)$
• B. $(v_1 -v_2 ):(v_2 -v_3 ) = ( t_1 +t_2) : (t_2 +t_3)$
• C. $(v_1 -v_2 ):(v_2 -v_3 ) = ( t_1 - t_2) : (t_2 + t_3)$
• D. $(v_1 -v_2 ):(v_2 -v_3 ) = ( t_1 +t_2) : (t_2 -t_3)$

Answer 1

The Correct Option is B

The correct answer is

Considering, u to be the initial velocity, then the following quotations can be obtained–

v₁ = u+at₁, v₂ = u+a(t₁+t₂), and v₃ = u+a(t₁+t₂+t₃)

Now, v₁ = (u+at₁)/2 = u+(u+at₁)/2 = u+1/2at₁

v₂= (v₁+v₂)/2 = u+at₁+1/2at₂

v₃= (v₂+v₃)/2 = u+at₁+at₂+1/2at₃

Now, v₁-v₂ = -1/2a(t₁+t₂)

v₂-v₃=  -1/2a(t₂+t₃)

Therefore,

Velocity measures how quickly an item shifts in relation to time. It is a vector quantity just like acceleration. It may be defined as the speed with which an action occurs or is completed. 

Keep in mind that speed and velocity are two distinct concepts. A scalar quantity, speed. 

The rate at which the speed and direction of an object's velocity vary with respect to time is known as its acceleration. It is by definition a vector quantity. 

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