Question

A body starting from rest from origin moves along x - axis with uniform acceleration. A, B, C and D are its positions after 15, 25, 3s and 4s respectively then OA : OB: OC: OD is
a)1:2:3:4
b)1:3:5:7
c)1:9:25:49
d)1:4:9:16
Pls answer with explanation
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Answer 1

Answer:

A is a right answers. dhighidhi

Answer 2

The ratio of OA: OB: OC: OD will be equal to 1: 4: 9: 16

Given:

The positions of A, B, C, and D are 1, 2, 3, and 4 respectively on the x-axis.

The body is starting from rest.

To Find:

The ratio of OA: OB: OC: OD

Solution:

It is very simple to solve this question as shown below,

We know that,

According to Newton’s laws of motion

$S = ut + \frac{1}{2}at^{2}$

Here u = 0

Then,

$S = \frac{1}{2}at^{2}$

This is a motion with uniform acceleration, hence the body displacement only depends on the time

That is,

S is directly proportional to $t^{2}$

$S$ ∝ $t^{2}$

It is already given that times are 1, 2, 3, and 4.

So,

The ratio of their time will be their squares.

That is,

= $1^{2}: 2^{2}: 3^{2}: 4^{2}$

= $1:4:9:16$

Hence, option (d) will be the correct answer.

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