Question

The acceleration ${}^{\prime }{a}^{\prime }$ and displacement ${}^{\prime }{x}^{\prime }$ are related to each other as $a=-x$. If the velocity of the particle is $u$ at zero displacement., then the distance covered by the particle to come to rest is equal to.

• A. $2u$
• B. $-7u$
• C. $u$
• D. $-u$

Answer 1

Answer: (C)

$u$

We know that if $x$ is displacement then we can write the acceleration as $a=v\frac{dv}{dx}$

bit this is given as $a=-x$ so $-x=v\frac{dv}{dx}$

or $-{\int }_{x=0}^{X}xdx={\int }_u^{0}vdv$

integrating above equation we will get $X=u$

so the distacne covered before coming to $rest$ is $u.$