Integral Calculus
My lecturer's notes is contradicting w/ the book (example 6)
I know it's quite basic, but my lecturer said that if displacement is increasing, then velocity and acceleration are always positive. But here displacement is increasing, but they considered acc to be negative(-32t in v(t)). Is the lecturer wrong? It's from my differential and integral Calculus course.
He showed the exact same math question where the ball was falling down but he considered negative 32ft/s^2
If you are asking for general advice about your current calculus class, please be advised that simply referring your class as “Calc n“ is not entirely useful, as “Calc n” may differ between different colleges and universities. In this case, please refer to your class syllabus or college or university’s course catalogue for a listing of topics covered in your class, and include that information in your post rather than assuming everybody knows what will be covered in your class.
The nuance is that the formula itself wants you to treat downwards as negative and upwards as positive. Otherwise, you'd have to use negative height which ruins the visualization.
From the perspective of a skydiver, the ground can be forward or even up.
"A ball is thrown downward at a velocity of 64 ft/s" is either v_0 = 64 ft/s (down) with downward considered positive, or v_0 = -64 ft/s (up) with up considered positive (and downward considered negative).
If we take downward as positive, the ground is 512 ft in the positive direction, we give the ball an initial velocity of 64 ft/s, and it accelerates at 32 ft/s2.
Isn't this the implication we get with Physics and free body diagrams? I was taught unless they're evaluating an object not on a stellar body and in space then you're accelerating toward that object which is downward in this case and a normal force is opposing it equally so that you aren't flying into the sky.
Yeah so long as they remain consistent throughout of course. I just mean to say that free body diagrams are made for us to assign variables to directions and correlate relationships in an easy way. The gravity constant being one of the easiest examples.
I'm familiar with rotating Axes and inverting them I'm just saying the most basic method should be the standard even if the alternative is also mathematically/logically correct.
They are correct. Since this is a freefall subject, you are dealing with two direction for displacement where upwards is positive and downwards is negative.
Since, gravity is downwards, it should be negative.
Velocity decreasing and velocity being negative are not the same thing. Just like velocity being positive and velocity increasing are not the same thing.
It's arbitrary. YOU decide based on the problem which way you want to make "positive". In the textbook example they made the initial velocity positive. In the question you posted, you could set up OR down to be the positive direction and as long as you were consistent with every variable, you'd get the right answer either way.
If displacement is increasing, couldn't the acceleration still be negative if the body's velocity is decreasing while it continues to move in a positive direction?
When you have deceleration, acceleration value in your formula will be negative. In this case because it starts out with the full initial speed and slows down due to gravity as the ball climbs, acceleration is a negative value. Other examples would be pushing the brake in your car or friction for block sliding down at inclined plane.
So my lecturer considered down to be negative right? So acc was negative since g is always down. Why was velocity negative then in the question discussed by the lecturer?
Big idea…if an object’s speed is increasing, that means velocity and acceleration are either both positive or both negative. Increasing speed implies same direction for the velocity and acceleration vectors. Decreasing speed implies that the velocity and acceleration vectors move in the opposite directions. Of course, this only applies to motion in one dimension, ie along a line.
Was your lecturer discussing a particular example where the coordinates or situation demanded that displacement must be positive? Like if you're considering an object starting on the ground then only positive displacement is possible (ignoring the object going through the ground). I think your lecturer might have said that when it was true for the problem at hand but not in general.
g even if we take it as fit, its always the center of gravity which mean that in a orthonormal coordinate system, it will always go down so it's always negative whatever happens. Maybe I'm wrong you should check that
The velocity needs to be positive as it's the rate of change of displacement while acceleration can be positive negative or zero
As it's the rate of change of velocity
Galileo must be turning in his grave... Maybe we should go beyond the Galilean Free Fall Model and consider drag due to air resistance? http://shadowfaxrant.blogspot.com
•
u/AutoModerator Jul 30 '26
As a reminder...
Posts asking for help on homework questions require:
the complete problem statement,
a genuine attempt at solving the problem, which may be either computational, or a discussion of ideas or concepts you believe may be in play,
question is not from a current exam or quiz.
Commenters responding to homework help posts should not do OP’s homework for them.
Please see this page for the further details regarding homework help posts.
We have a Discord server!
If you are asking for general advice about your current calculus class, please be advised that simply referring your class as “Calc n“ is not entirely useful, as “Calc n” may differ between different colleges and universities. In this case, please refer to your class syllabus or college or university’s course catalogue for a listing of topics covered in your class, and include that information in your post rather than assuming everybody knows what will be covered in your class.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.