Question

TOPIC: DIFFERENTIATION AND INTEGRATION IN KINEMATICS

A point moves along a straigth line with retardation which depends on the velocity as f =a√v. Where 'a' is a
constant. If the initial velocity of point is V1, in what time will
it come to rest?
options:
1. V1/a
2. 2√V1/a
3.2V1/a
4.√V1/a

I need genuine answers with explanation ...if you spam answers I'll report ​

solve kardo yaar ..I've been trying the question for past 20 mins

Answer 1

Step-by-step explanation:

We have,

$f = - a \sqrt{v}$

$\frac{dv}{dt} = - a \sqrt{v}$

$\implies \frac{dv}{ \sqrt{v} } = - a dt$

$\implies \int^{0}_{v _{1} } \frac{dv}{ \sqrt{v} } = - \int^{t}_{0} a dt$

Here, 't' is the required time,

$\implies 2 [ \sqrt{v} ]^{0}_{v _{1} } = - a [ t] ^{t}_{0}$

$\implies - 2 \sqrt{v_{1} } = - a t$

$\implies t = \frac{2}{a} \sqrt{v_{1} }$