# Which moves faster in a time $t$: $A$ or $B$? [closed]

Suppose we have two objects, $A$ and $B$, both made of the same substance. They also have the same shape (e.g. two spheres), but $A$ is larger and therefore more massive than $B$.

Both $A$ and $B$ are subjected to a constant force for a time $t$, through the same medium. Both are subject to drag from the medium - suppose this is a fluid drag. Which object covers the most distance in time $t$?

• What you need to know to solve this is that the drag on a sphere is given by $F_d = \tfrac{1}{2}C_d \rho A v^2$, where $A$ is the cross sectional area $\pi r^2$ and $v$ is the velocity. $C_d$ is a constant and $\rho$ is the fluid density - neither of these depend on the size of the sphere. Commented Oct 20, 2014 at 15:43

B will move faster, the reason is that the acceleration, $a$, of A is smaller for two reasons (remember that $F_{applied}-F_{drag}=ma$) : 1) the same force forward is applied so the contribution to the acceleration on the smaller ball will be larger 2)the drag force on the larger ball will be larger (see Rennie's comment) on A because the cross sectional area is larger.