We're out currently because of Coronavirus so all of my assignments are online because we're stuck inside. I was struggling before when I had a teacher, but I'm really struggling now without. He's linking most of our assignments to this site called Physicsclassroom. I can probably do the majority on my own, but I need help getting there with explanations. Being limited, there's only so many options i have as to get help on them. Please, if there's anyone that can help, I'd greatly appreciate it. Thank you.
The options are $\Delta V$, Time, or Mass for the first one. After that, they're either of the cases: case A or case B.
In first question, the time of collision is given to be same, the mass cannot change during a collision (conservation of mass), so it is the velocity that changes (which it clearly changes from 18$\hat{i}$ to $-6\hat{i}$, and 18$\hat{i}$ to 0 as given) So $\Delta v$ is the correct option here.
The momentum change in Case A is $\Delta \overrightarrow{p} = m(\overrightarrow{v_{final}}-\overrightarrow{v_{initial}} )= 1200(-6\hat{i} -18\hat{i})=1200(-24\hat{i}) $
In case B, $\Delta \overrightarrow{p} = m(\overrightarrow{v_{final}}-\overrightarrow{v_{initial}} )= 1200(0 -18\hat{i})=1200(-18\hat{i}) $
So for the second question, case A has larger momentum change.
For third question, by the impulse momentum theorem (Impulse = change in momentum), Case A has larger impulse recieved on the car.
Lastly, Impulse is nothing but force times the time of collision, so force will also be larger in case A (as the time of collision is same)
BTW, try to ask questions that involve purely physics on the physics page of stack exchange: Link to the Physics Page