Question

14 mark for review a train travels in the +x - direction with speed v_t relative to the ground. a passenger on the train rolls a ball across a level table in the -x - direction at a constant speed v_0 relative to the train. another passenger quickly stops the ball and rolls it back with the same speed v_0 relative to the train. which of the following graphs could represent the x - component of the velocity of the ball relative to the ground as a function of time? a velocity (relative to the ground) v_t time b velocity (relative to the ground) v_t time

Explanation:

Step1: Analyze initial velocity

The train is moving in the +x - direction with speed $v_t$ relative to the ground. When the ball is rolled in the -x - direction on the train with speed $v_0$ relative to the train, the velocity of the ball relative to the ground is $v = v_t - v_0$.

Step2: Analyze when ball is stopped

When the ball is quickly stopped on the train, its velocity relative to the train is 0, so its velocity relative to the ground is $v_t$.

Step3: Analyze when ball is rolled back

When the ball is rolled back in the +x - direction on the train with speed $v_0$ relative to the train, its velocity relative to the ground is $v = v_t + v_0$.

The ball's velocity relative to the ground first has a value of $v_t - v_0$ (when rolled in -x - direction on train), then $v_t$ (when stopped on train) and then $v_t + v_0$ (when rolled back in +x - direction on train).

Answer:

The graph that shows a lower - constant velocity first, then a middle - constant velocity and then a higher - constant velocity as time progresses is the correct one. Without seeing all the options completely, but based on the analysis, the velocity of the ball relative to the ground changes in steps as described above.