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Answer One of the Students' Questions, and Ask Another

Student "edition" found at {csi dot journalspace dot com}.

Maybe I shouldn't have started this blog now, not with everything that's been going on.

The second session of the sixth week of classes for my mechanics lecture students was their first long exam, which is a hundred points compared to the fifty point quiz that we had last time. There were five problems, some with their own sub-questions, so it still totaled a little more than a hundred points, which was, as usual, my bonus for them.

I even gave them a little situation clarification for the first one, where in this car started braking and decelerating when the driver sees that an obstacle is in his path a certain distance away. So given the rate of deceleration, they had to figure out if it would still hit the object or not.

Admittedly, this is the same kind of problem that I also gave to one of my mechanics lecture classes two terms ago. So if there was anyone from my current class who asked around from the previous takers of the subject, it would have been a great addition to their studies and their scores to have done that kind of research.

One of the students though, asked my why he was getting a negative value inside the square root symbol for that problem.

I told him to go about it one of two ways: first, treat his analysis as wrong and come up with another equation and use different given. This was because he used the distance of the car to the object as the real displacement, which is not the case. One procedure of going about it would have been to solve for the displacement to stopping (or final velocity zero) of the car then comparing it with the distance to the object.

I actually told them this in the clarification I gave. If the displacement is larger than the distance, then the car hits the object. If the displacement is smaller than the distance, it means the car was able to stop before it hit the object.

The second method was to stay with the same solution and just come up with his own conclusion: this was that since it was mathematically impossible to solve for a numeric value for the time at which the car travels the distance to the object, then that means that the car’s actual duration must have been smaller than the distance to the object.

There was another reused situation from previous classes of an object getting thrown straight up and hitting the ceiling, which is definitely different from our previous examples of an object hitting the ground.

This is where their analysis of the previous problems we had should have helped them eliminate the wrong scenarios and determine the correct solution.

Session 821 decelerates and stops before reaching the object in its path. Class dismissed.


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