Question

In the one-dimensional motion of a particle, the relation between position x and time t is given by $x^2+2x=t$ (here x >0). Choose the correct statement :

• A. The retardation of the particle is $\frac{-1}{4(x+1{)}^3}$
• B. The uniform acceleration of the particle is $\frac{1}{(x+1{)}^3}$
• C. The uniform velocity of the particle is $\frac{1}{(x+1{)}^3}$
• D. The particle has a variable acceleration of 4t+6.

Answer 1

The correct option is A The retardation of the particle is $\frac{-1}{4(x+1{)}^3}$

$x^2+2x=t$ $;$ $x$ is distance and $t$ is time

$\Rightarrow 2x.v+2v=1$ ( Difference between t )

$\Rightarrow v=\frac{1}{(x+1)2}$

$\Rightarrow a=\frac{dx}{dt}=\frac{-1}{2{(x+1)}^2}\times v$

$=\frac{-1}{{(x+1)}^2}\times \frac{1}{2(x+1)}$

$\Rightarrow a=\frac{-1}{4{(x+1)}^3}$

The retardation of the particle is $\frac{-1}{4{(x+1)}^3}.$