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

Question

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

Let u be the initial velocity ∴ v1=u+a t1, v2=u+a(t1+t2) and v3=u+a(t1+t2+t3) Now v1=(u+v1/2)=(u+(u+a t1)/2)=u+(1/2) a t1 v2=(v1+v2/2)=u+a t1+(1/2) a t2 v3=(v2+v3/2)=u+a t1+a t2+(1/2) a t3 So (v1-v2)=-(1/2) a(t1+t2) and (v2-v3)=-(1/2) a(t2+t3) ∴ (v1-v2):(v2-v3)=(t1+t2):(t2+t3)

Q. A point moves with uniform acceleration and $v_{1}$ , $v_{2}$ and $v_{3}$ denote the average velocities in the three successive intervals of time $t_{1}$ , $t_{2}$ and $t_{3}$ . Which of the following relation is correct?

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

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

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

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

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

(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​)

Q. A point moves with uniform acceleration and $v_{1}$ , $v_{2}$ and $v_{3}$ denote the average velocities in the three successive intervals of time $t_{1}$ , $t_{2}$ and $t_{3}$ . Which of the following relation is correct?

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

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

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

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