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 larger mass will have less inertia 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 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 constant, $a=\frac{F}{m}$.

Step2: Analyze acceleration for different masses

Since $F$ is the same for both trains, and $a=\frac{F}{m}$, the train with smaller mass will have a larger acceleration (because mass $m$ is in the denominator).

Step3: Relate acceleration to stopping time

Using the kinematic equation $v = v_0+at$ (when stopping, final velocity $v = 0$). For the same initial velocity $v_0$, a larger acceleration $a$ means a shorter time $t$ to stop ($t=\frac{v_0 - v}{a}$). So the train with smaller mass will require less time to stop.

Answer:

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