Question

A particle starts moving from rest under uniform acceleration. It travels a distance $x$ in the first two seconds and a distance y in the next two seconds. If $y=nx$, then $n$ is equal to_____

A) 1

B) 2

C) 3

D) 4

Answer 1

Hint: To solve this question first we will find distance covered by partile in the first two second and next two second then we relate both distances according to the given relation and finally we will get the value of n.

Formula used: 

Here, we will use the equation of motion:

$s = ut + \dfrac{1}{2}a{t^2}$

Here, $s$ is the distance travelled

$u$ is the initial velocity

$t$ is the travel time

$a$ is the acceleration of the particle.

Complete step by step answer:

We will start by considering the acceleration to be $a$,

Given, the initial velocity is 0.

The distance travelled in first two seconds, x,

So, $x = u\left( 2 \right) + \dfrac{1}{2}a{\left( 2 \right)^2} = \dfrac{1}{2}\left( {4a} \right)$

Similarly, the distance to be travelled in next two seconds, y = distance travelled in four seconds − distance travelled in two seconds,

$y = \left[ {4u + \dfrac{1}{2}a{{\left( 4 \right)}^2}} \right] - \left[ {2u + \dfrac{1}{2}a{{\left( 2 \right)}^2}} \right]$

$ \Rightarrow y = \dfrac{1}{2}a\left( {{4^2} - {2^2}} \right) = 6a$

Now we need the ratio of y and x:

$\dfrac{y}{x} = \dfrac{{6a}}{{2a}} = 3$

Thus, the value is $y=3x$, and so $n=3$

The correct option is (C).

Additional Information: 

Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance.

The first scientist to measure speed as distance over time was Galileo.

Time in physics is defined by its measurement: time is what a clock reads. In classical, non-relativistic physics, it is a scalar quantity and, like length, mass, and charge, is usually described as a fundamental quantity.

Note: 

In Mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the orientation of the net force acting on that object.