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...

1 year ago

Answered by Peter, an A Level Maths tutor with MyTutor

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


£20 /hr

Tiarnan B.

Degree: MChem (Masters) - York University

Subjects offered: Maths, Geography+ 2 more

-Personal Statements-

“About Me: I am a student of Chemistry at the University of York studying for a masters degree and am a self-confessed science nerd! My goal is to give you the help you need, build your confidence and push you to be the best you can. A...”

£22 /hr

Joe B.

Degree: Mathematics G100 (Bachelors) - Bath University

Subjects offered: Maths, Further Mathematics + 4 more

Further Mathematics
-Personal Statements-

“About Me Hi, I'm Joe, a first year mathematics student from Luton studying at Bath University. I am an accomplished mathematician and economist, having achieved A* grades in A Level Maths, Further Maths and Economics in June 2016. As ...”

£24 /hr

Elizabeth G.

Degree: Mathematics (G100) (Bachelors) - Durham University

Subjects offered: Maths, Science+ 2 more


“ Hello, my name is Elizabeth, I am studying maths at Durham. I love maths but also studied chemsitry and physcis at A-level. I have two younger sisters who I have helped through similar exams and have tutored various other subjects giv...”

About the author

£20 /hr

Peter W.

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

Subjects offered: Maths, Physics+ 1 more

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

How to get A and A* in Maths?

Find the integral of 3x^2 + 4x + 9 with respect to x.

What methods are there for integration?

Solve the differential equation: e^(2y) * (dy/dx) + tan(x) = 0, given that y = 0 when x = 0. Give your answer in the form y = f(x).

View A Level Maths tutors


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