Question

9. For a body starting from rest and moving with uniform acceleration, the ratio of
displacement covered in 1st, 2nd, 3rd second is
CA 1 .2 .3 :
(B) 1:4:9:....
(C) 2:4:7:
(D) 1:3:5:....
ES​

Answer 1

▶Solution :

Given :

A body starting from rest (initial velocity = zero) and moving with uniform acceleration.

To Find :

The ratio of distance cevered in first, second and third second.

Formula :

Formula of distance covered by moving body in nth second of journey is given by

$\underline{\boxed{\bf{\pink{d_n=u+\dfrac{a}{2}(2n-1)}}}}$

• u denotes initial velocity
• a denotes acceleration
• n denotes no. of second
• d denotes distance

Calculation :

Since, acceleration has constant magnitude throughout the whole journey, we can say that...

$\star\bf\:\blue{d_n\varpropto(2n-1)}\\ \\ \rightarrow\sf\: d_1 : d_2 : d_3=[2(1)-1 ]: [2(2)-1] : [2(3)-1]\\ \\ \rightarrow\sf\:d_1:d_2:d_3=(2-1) : (4-1) : (6-1)\\ \\ \rightarrow\underline{\boxed{\bf{\purple{d_1:d_2:d_3=1:3:5}}}}$

✒ Option D) is correct