# A particle starts from rest and moves in a st. line with velocity given by dx/dt=(x+1) where x is the distance transversed in time t seconds the time taken by the particle to traverse a distance of 999 metres is

Solution:

$\frac{dx}{(x+1)}=dt$

Integrating , we get

$t+c=\log_{e}(x+1)$

For   $t=0,x=0\Rightarrow c=0$     $........(1)$

$\therefore (1)$  becomes

$t=\log_{e}(x+1)$       $.........(2)$

For    $x=999$

$t=\log_{1000}=3\log_{e}10.$

## Most Viewed Questions

### Preparation Products

##### Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
##### Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
##### Knockout NEET (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
##### Knockout NEET (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-