Question

two trains are traveling down a track. train a has more mass than train b. what will happen when the two trains attempt to stop with the same force at the train station? the train with the larger mass will require less time to stop than the train with the smaller mass. the train with the smaller mass will require less time to stop than the train with the larger mass. the train with the larger mass will have less inertia than the train with the smaller mass. the train with the smaller mass will take longer to stop than the train with the larger mass.

Explanation:

Step1: Recall Newton's second law

$F = ma$, where $F$ is force, $m$ is mass and $a$ is acceleration. When $F$ is the same, a larger $m$ results in a smaller $a$.

Step2: Analyze stopping - time

The time $t$ to stop can be related to acceleration. Using the kinematic equation $v = v_0+at$ (when stopping, final velocity $v = 0$). Rearranging for $t$ gives $t=\frac{v_0 - v}{a}$. A smaller acceleration $a$ (for larger - mass train) means a longer time to stop when the initial velocity $v_0$ is the same. Also, inertia is directly related to mass, so a larger - mass train has more inertia.

Answer:

The train with the smaller mass will require less time to stop than the train with the larger mass.