If the unit of length is doubled and the unit of time is halved, the unit of velocity will be changed by what factor?

Solution

1. Velocity $v$ is defined as $v=L/T$.
2. Let the new length be $L^{\prime }=2L$ and the new time be $T^{\prime }=T/2$.
3. The new velocity is $$\begin{array}{rl}{v}^{\prime }& =L^{\prime }/T^{\prime }\\ & =(2L)/(T/2)\\ & =4(L/T)\end{array}$$.
4. Thus, $v^{\prime }=4v$.
5. Hence the answer is (B).