A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to

Question

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $v(x)=\alpha x^{3n}$, where $\alpha$ and $n$ are constants and $x$ is the position of the particle. The acceleration of the particle as a function of $x$, is given by

Professor PC Thomas Classes · Answer

(a) : According to question, velocity of unit mass varies as $v(x)=\alpha x^{3n}$ \ $\frac{d v}{d x} = 3 n \alpha x^{3n-1}$ \ Acceleration of the particle is given by $a = \frac{d v}{d t} = \frac{d v}{d x} 	imes \frac{d x}{d t} = v \frac{d v}{d x}$ \ Substituting the values, we get: \ $a = (\alpha x^{3n}) 	imes (3 n \alpha x^{3n-1}) = 3 n \alpha^{2} x^{6 n-1}$