An object is dropped from rest at $t=0$ near Earth's surface and experiences a resistive force of magnitude $kv,$ where $v$ is the speed of the object and $k$ is a constant which depends on a variety of factors. The object reaches a speed of $0\mathrm{.}5v_T$ at $t=t_{0\mathrm{.}5},$ where $v_T$ is the object's terminal velocity. If another object has the same mass but a greater value of $k,$ what changes would occur to the terminal speed, $v_T,$ and the time it takes to get to half the terminal speed, $t_{0\mathrm{.}5}?$