A particle starts with a velocity of 2 m/s and moves in a straight line with a retardation of 0.1 `m/s^2`. the time that it takes to describe 15 m is : Options: A . &nbsp10 s in its backward journey. B . &nbsp30 s in its forward journey C . &nbsp10 s in its forward journey D . &nbsp30 s in its backward journey E . &nbspboth )b) and (c) are correct.

A particle starts with

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Question -

A particle starts with a velocity of 2 m/s and moves in a straight line with a retardation of 0.1 `m/s^2`. the time that it takes to describe 15 m is :

Options:

A . 10 s in its backward journey.

B . 30 s in its forward journey

C . 10 s in its forward journey

D . 30 s in its backward journey

E . both )b) and (c) are correct.

Answer: Option D

Sol. Le the particle returns back after time t = `t_0`

For this , v = 0, at t = `t_0`

v = u + a

or 0 = 2 - 0.1`t_0`

`t_0 = 2/0.1 = 20` sec.

s = ut + `1/2 at^2`

or ` 15 = 2 - 1/2 0.1t^2`

or `30 = 4t - 0.1t^2`

or `300 = 40t - t^2`

or `t^2 - 40 t + 300 = 0`

`:.` t = `(40 pm sqrt(1600 - 1200))/(2 xx 1)`

= `(40 pm 20)/(2 )`

`:.` t = 30 sec or 10 sec.

Hence , (d) is correct .

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