Acceleration has dimension [L/T2]. Use dimensional analysis to determine the ratio of accelerations for car A to car B, if, everything else being equal, car A travels a given distance in half the time required by car B.
A) 4
B) $1 / \sqrt{2}$
C) $\sqrt{ } 2$
D) $1 / 2$
E) $1 / 4$
F) 2

Question

Quizplus · Accepted Answer

Acceleration is given by the formula $a = \frac{2d}{t^2}$, where $d$ is distance and $t$ is time. If car A travels the same distance in half the time of car B, then $t_A = \frac{1}{2}t_B$. Substituting into the acceleration formula gives $a_A = \frac{2d}{(\frac{1}{2}t_B)^2} = \frac{2d}{\frac{1}{4}t_B^2} = 8 \cdot \frac{2d}{t_B^2} = 4a_B$. Therefore, the ratio of accelerations $a_A/a_B$ is 4.

Acceleration Has Dimension [L/T2] 1/21 / \sqrt{2}1/2​ C) 2\sqrt{ } 2​2 D) 1/21 / 21/2

Acceleration Has Dimension [L/T2] $1 / \sqrt{2}$ C) $\sqrt{ } 2$ D) $1 / 2$