MYTUTOR SUBJECT ANSWERS

870 views

How do I calculate the rate of change of something for which I don't have an equation?

This kind of question is an application of differentiation. If t represents time, any derivative with respect to t is a rate of change. For example, if h represents the depth of water in a cubicle container, dh/dt is the change in depth over time, or the rate of change of the depth in other words. If the question does not give you an equation that directly relates the thing you want the rate of change of to time, it will often give you an equation that relates a different quantity to time. For example, it might ask you to calculate the rate of change of volume of water in the container, but not give you an equation for volume in terms of time, and so one differentiation won't suffice. I find it really helpful to write out what I'm trying to calculate and how I could do so with the given terms. Let's say we need to calculate the rate of change of volume of water in the container. We are given that the rate of change of depth (dh/dt) is 10m/s, and that the container is a cuboid with dimensions of 50x50xh m. We want dV/dt. We have dh/dt, so if we write this out we know that dV/dt = (dh/dt)*(some other derivative). If you treat derivatives as fractions (which you normally can), you can see that in order cancel out dh, the other derivative must be dV/dh. We know that the equation for volume in terms of h for a cuboid of dimensions 50x50xh is simply V=2500h. Differentiate this and you get dV/dh=2500. All that's left to do is to multiply the two derivatives together, so dV/dt=10*2500 = 25000. So the rate of change of volume is 25000m^3/s.

Sam E. A Level Extended Project Qualification tutor, A Level Physics ...

2 years ago

Answered by Sam, an A Level Maths tutor with MyTutor


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

296 SUBJECT SPECIALISTS

£20 /hr

Elizabeth P.

Degree: Geophysics (Bachelors) - Durham University

Subjects offered:Maths, -Personal Statements-

Maths
-Personal Statements-

“Hey there! My name is Libby and I’m currently in my final year studying Geophysics at Durham university. I love to get other people as excited about maths and science as I am and have done so by tutoring at school, being involved outr...”

MyTutor guarantee

£30 /hr

Joe D.

Degree: Philosophy, Politics and Economics (Bachelors) - Durham University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Chemistry
Biology

“About Me:I am currently studying Philosophy, Politics and Economics at Durham University. So although I now specialise in humanities, I have continued to study the sciences simultaneously and mydepth of experience will enable me to h...”

£22 /hr

Elliot J.

Degree: Computer Science (Bachelors) - Durham University

Subjects offered:Maths, Science+ 1 more

Maths
Science
Physics

“I study Computer Science. I’m a keen mathematician and previous GCSE maths tutor. I play various sports and piano. I am also an aspiring photographer.”

MyTutor guarantee

About the author

Sam E.

Currently unavailable: no new students

Degree: Physics with Australian Study (Masters) - Exeter University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Extended Project Qualification

“Hi, I'm Sam. I'm studying for a Masters in Physics at the University of Exeter. I love space, and hope to go into the field of scientific research in space sciences. I'll use this passion for my subject to tutor Maths, Physics and EPQ.”

MyTutor guarantee

You may also like...

Posts by Sam

How do I calculate the rate of change of something for which I don't have an equation?

How do I manage the workload of an EPQ alongside other A-levels?

What is the main evidence for the Big Bang theory?

Other A Level Maths questions

C1 - Simplifying a fraction that has a root on the denominator

Integrate 1/(5-2x) for 3≤x≤4

Show that sin2A is equal to 2sinAcosA

Differentiating (x^2)(sinx) Using the Product Rule

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