MYTUTOR SUBJECT ANSWERS

602 views

How does finding the gradient of a line and the area under a graph relate to real world problems?

Practical applications of calculus occur more often than you would think. The most common example of them being applied to real world problems is through the relationship between distance and time. The distance an object will travel in a certain time is it's velocity. If we differentiate an equation for distance travelled with respects to time, it will give an equation for velocity.
However this is only useful if the objects velocity is constant; it could be speeding up (acccelerating). The acceleration of a body is it's change in speed over time. So, if we differentiate an equation for velocity with respects to time, it will give an equation for acceleration.
You can differentiate again to give the rate of change of acceleration, but this is a less useful figure to be given.
Conversely, if you have an equation for an object's acceleration, you can integrate it (the opposite of differentiating it) with respects to time to give an equation for it's velocity at a certain time.
Integrating again will give the distance it has travelled after a certain time.
Calculus can be used in this way in loads more equations including  force-energy-power, and circumference-area in a circle.
All of these values can be plotted on graphs, and different features of a particular graph (such as the gradient of the line and the area under it) will give you these values. Remember, a graph is just a visual representation of an equation, so that's where they come into it.

Peter W. A Level Maths tutor, A Level Further Mathematics  tutor, A L...

2 years ago

Answered by Peter, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

269 SUBJECT SPECIALISTS

£26 /hr

Martyna S.

Degree: Neurotechnology (Masters) - Imperial College London University

Subjects offered:Maths, Science+ 4 more

Maths
Science
Chemistry
Biology
.BMAT (BioMedical Admissions)
-Personal Statements-

“PhD candidate in Bioengineering at Imperial College London. Long experience in effective tutoring!”

£30 /hr

Ayusha A.

Degree: BEng electrical and electronics engineering (Bachelors) - Newcastle University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“About me: I am a final year Electrical and Electronic Engineering student at Newcastle University. I took Mathematics, Further Mathematics, Chemistry and Physics as my A-level subjects. I did peer mentoring in university and also have...”

£20 /hr

Juris B.

Degree: Computer Science (Bachelors) - St. Andrews University

Subjects offered:Maths, Computing

Maths
Computing

“I am a Computer Science at the University of St. Andrews. Before that however, I was a pupil in a school in the North-East of Scotland. With the combined passion and availability of superb teachers - I was given an opportunity to exce...”

About the author

Peter W.

Currently unavailable: for new students

Degree: Aerospace Engineering (Masters) - Queen's, Belfast University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Second year Aerospace Engineering student at Queen's University Belfast. Happy to offer help in Maths, Further Maths and Physics at GCSE and A-Level, which I have great experience in both learning and tutoring.”

You may also like...

Posts by Peter

How do you plot a complex number in an Argand diagram?

How does finding the gradient of a line and the area under a graph relate to real world problems?

Other A Level Maths questions

Given that (2x + 11 )/(2x + 1)(x + 3) ≡ A /(2x + 1) + B /(x + 3) , find the values of the constants A and B. Hence show that the integral from 0 to 2 (2x + 11)/ (2x + 1)(x + 3) dx = ln 15.

How do you use trigonometry to work out angles and lengths of sides in a right angle triangle

How do I multiply complex numbers?

What is a logarithm?

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok