A ball of mass 1 kg moves in a straight line with velocity $v=c x^\alpha$, where $c=1$ (SI unit) and $\alpha$ is a constant. If the work done by the net force during its displacement from $x=0$ to $x=4 \mathrm{~m}$ is 128 J , then the $\alpha$ is

The potential energy of an object is $U(x)=\left(5 x^2-4 x^3\right) \mathrm{J}$, where $x$ is the position in metre. The position at which the force becomes zero is

Identify the incorrect statement.

A force acts on a 30 g particle in such a way that the position of the particle as a function of time is given by $x=\alpha t^2$, where $x$ is in metre, $t$ is in seconds and $\alpha=1 \mathrm{m} / \mathrm{s}^2$. The work done during the first 4 s is