Find an expression for the velocity and the acceleration at any time. Find the velocity and acceleration after ${\displaystyle 10}$ seconds.

(10) A body moves in such a way that the spaces described in the time ${\displaystyle t}$ from starting is given by ${\displaystyle s=t^{n}}$, where ${\displaystyle n}$ is a constant. Find the value of ${\displaystyle n}$ when the velocity is doubled from the ${\displaystyle 5}$th to the ${\displaystyle 10}$th second; find it also when the velocity is numerically equal to the acceleration at the end of the ${\displaystyle 10}$th second.