When the ball bounces on the wall, could we also have said that the velocity changes from v to -v? I don't understand how the wall causes it to change from 0 to v because the ball has a velocity when it hits the wall
Yeah you could use v and -v for the bouncing scenario, but then your delta v magnitude is 2v (-v-v=-2v). Whereas the ball rolling down the hill has a delta v magnitude of v (v-0=v). Your goal in this question part is to compare accelerations in both scenarios. Im using accel=delta v/t, and the problem with the way you suggested is that your delta v and t would be different for both scenarios. You effectively have three variables. Convincing arguments use two variables, a dependent and an independent, with some value being constant between the two scenarios. That is why I used the the time interval where the ball is fully compressed to when it bounces off the wall (-v-0=-v), producing a delta v magnitude of v, just like the ball rolling down the hill. Therefore, when I use accel=delta v/t, I can consider the delta v being constant in both situations and just examine how the time is different in each scenario (independent variable) and see how that affects the acceleration for each scenario (dependent variable).
When the ball bounces on the wall, could we also have said that the velocity changes from v to -v? I don't understand how the wall causes it to change from 0 to v because the ball has a velocity when it hits the wall
Yeah you could use v and -v for the bouncing scenario, but then your delta v magnitude is 2v (-v-v=-2v). Whereas the ball rolling down the hill has a delta v magnitude of v (v-0=v). Your goal in this question part is to compare accelerations in both scenarios. Im using accel=delta v/t, and the problem with the way you suggested is that your delta v and t would be different for both scenarios. You effectively have three variables. Convincing arguments use two variables, a dependent and an independent, with some value being constant between the two scenarios. That is why I used the the time interval where the ball is fully compressed to when it bounces off the wall (-v-0=-v), producing a delta v magnitude of v, just like the ball rolling down the hill. Therefore, when I use accel=delta v/t, I can consider the delta v being constant in both situations and just examine how the time is different in each scenario (independent variable) and see how that affects the acceleration for each scenario (dependent variable).