# Equation of motion and Calculus

1. Sep 15, 2015

### Jamie S

• HW Template missing as it was moved from another forum
Hi all,

I started a level 3 btech in mech engineering and today was my first physics class. All went well apart from the tricky question at the end of class.

I thought it was a good idea to ask the question "how much harder can this be from last year".
Turns out for me not being brilliant at calculus it can be much harder.

The question surrounded the formula s=ut+1/2at^2
I was asked to differentiate s with respect to t, and show displacement is a minimum when u= - at

Off course it was a disaster and i laughed it off has not being forced to answer the question at which point other pupils attempted it.

We never did have it explained fully but it has made me wonder how one would go about answering this using differentiation. Ive used algebra and transposed the formula before but this is the first time ive seen it this way.

It all got a little bit more confusing when someone suggested that it cant be differentiated until its been integrated. Is there any truth in this?

Cheers

2. Sep 15, 2015

### Staff: Mentor

Well, you are given displacement as a function of t. Can you take the derivative? (How do you find the max / min values of a function using calculus?)

No idea what that is supposed to mean. Ignore it.

3. Sep 15, 2015

### Jamie S

the only time ive taken min and max values was by using a quadratic equation

4. Sep 15, 2015

### Staff: Mentor

This will be easier.

5. Sep 15, 2015

### Jamie S

using quadratic formula was suggested however it was insisted that differentiation be used.

im looking at my notes from mondays math and the handout i recieved with calculus rules.
isnt the derivative of a function normally dy/dx = ....
in this case would that be;
ds/dt = ut+1/2at^2

6. Sep 15, 2015

### Staff: Mentor

No, that right hand side is s, not ds/dt. You start with the function s, which is given, and take the derivative.

7. Sep 15, 2015

### Jamie S

i dont quite follow

8. Sep 15, 2015

### SteamKing

Staff Emeritus
Or, more to the point, if s = ut + (1/2)*a*t2 and you take the derivative of s with respect to t to find ds/dt, you must do the same to the right hand side of the equation.

9. Sep 15, 2015

### Staff: Mentor

Are you saying that you have not yet had calculus?

Chet

10. Sep 15, 2015

### Jamie S

ive had one mathematics class up to now. very little on my level 2.

11. Sep 15, 2015

### Jamie S

you no i am aware that i will need to improve drastically if im to ever progress from this level. at the moment through weve not touched on any calculus though we have only just enrolled monday.

12. Sep 15, 2015

### Staff: Mentor

Here's what I understand from what you said in your previous two posts: You never had calculus in any of your courses before, and today is only your second day in a calculus course. If that is the case, then you are not going to be able to solve this problem using calculus.

Chet

13. Sep 15, 2015

### Jamie S

Chestermiller... I take your comments and while i may or may not have had enough time using calculus my initial intention was never to solve this equation. I did however ask about it because i was curious of how it would be solved using the calculus method. It isn't homework or course work, i at least hope so given ive just started the course so i didnt see were there would be hesitation to answer.

I thank all that have made the effort to comment and suggest solutions.

14. Sep 15, 2015

### Staff: Mentor

Hi Jamie,

I'm proud of your agressiveness for being so interested in seeing how calculus might be applied to problem, even before you have studied calculus. Bravo. My advice is to just be patient and, in almost no time (probably in just a few weeks), you will be be solving problems like this on your own. Best of luck in your calculus course.

Chet