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Physics Question on Motion in a straight line

A point moves with uniform acceleration v1,v2v_1,v_2 and v3v_3 denote the average velocities in three successive intervals of time t1,t2t_1, t_2 and t3t_3. Correct relation among the following is

A

(v1−v2):(v2−v3)=(t1−t2):(t2−t3)(v_1 -v_2 ):(v_2 -v_3 ) = ( t_1 -t_2) : (t_2 -t_3)

B

(v1−v2):(v2−v3)=(t1+t2):(t2+t3)(v_1 -v_2 ):(v_2 -v_3 ) = ( t_1 +t_2) : (t_2 +t_3)

C

(v1−v2):(v2−v3)=(t1−t2):(t2+t3)(v_1 -v_2 ):(v_2 -v_3 ) = ( t_1 - t_2) : (t_2 + t_3)

D

(v1−v2):(v2−v3)=(t1+t2):(t2−t3)(v_1 -v_2 ):(v_2 -v_3 ) = ( t_1 +t_2) : (t_2 -t_3)

Answer

(v1−v2):(v2−v3)=(t1+t2):(t2+t3)(v_1 -v_2 ):(v_2 -v_3 ) = ( t_1 +t_2) : (t_2 +t_3)

Explanation

Solution

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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