A point moves with uniform acceleration v1,v2 and v3 denote the average velocities in three successive intervals of time t1, t2 and t3 . Correct relation among the following is

Question

A point moves with uniform acceleration v1,v2 and v3 denote the average velocities in three successive intervals of time t1, t2 and t3 . Correct relation among the following is (A) (v1 -v2 ):(v2 -v3 ) = ( t1 -t2): (t2 -t3) (B) (v1 -v2 ):(v2 -v3 ) = ( t1 +t2): (t2 +t3) (C) (v1 -v2 ):(v2 -v3 ) = ( t1 - t2): (t2 + t3) (D) (v1 -v2 ):(v2 -v3 ) = ( t1 +t2): (t2 -t3)

Tardigrade Admin · Accepted Answer

Vavg = (ut + (1/2) at2/t) = u + (1/2) at ν1 = u + (1/2) at1 ........(1) ν2 = ν1 + (1/2) at2 .......(2) ν3 = ν2 + (1/2) at3 .......(3)

Q. 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

$(v_{1} - v_{2}) : (v_{2} - v_{3}) = (t_{1} - t_{2}) : (t_{2} - t_{3})$

$(v_{1} - v_{2}) : (v_{2} - v_{3}) = (t_{1} + t_{2}) : (t_{2} + t_{3})$

$(v_{1} - v_{2}) : (v_{2} - v_{3}) = (t_{1} - t_{2}) : (t_{2} + t_{3})$

$(v_{1} - v_{2}) : (v_{2} - v_{3}) = (t_{1} + t_{2}) : (t_{2} - t_{3})$

$V_{a vg} = \frac{u t + \frac{1}{2} a t ^{2}}{t} = u + \frac{1}{2} a t$
$ν_{1} = u + \frac{1}{2} a t_{1}$ ........(1)
$ν_{2} = ν_{1} + \frac{1}{2} a t_{2}$ .......(2)
$ν_{3} = ν_{2} + \frac{1}{2} a t_{3}$ .......(3)

Q. A point moves with uniform acceleration v1​,v2​ and v3​ denote the average velocities in three successive intervals of time t1​,t2​ and t3​. Correct relation among the following is

(v1​−v2​):(v2​−v3​)=(t1​−t2​):(t2​−t3​)

(v1​−v2​):(v2​−v3​)=(t1​+t2​):(t2​+t3​)

(v1​−v2​):(v2​−v3​)=(t1​−t2​):(t2​+t3​)

(v1​−v2​):(v2​−v3​)=(t1​+t2​):(t2​−t3​)