Physics and Maths in Singapore

Dr Hock

I am a science graduate with a first class honours and a physics PhD from Cambridge University. In these webpages, you will find information about me and my notes and videos.

Videos and notes

I have recorded a set of videos on A level physics. You may also find something useful on other topics in physics and mathematics that I am still developing.


For enquiries, please visit my contact page.

Here are a few of my A level physics videos:

Newton's Law of Gravitation
Constructive and Destructive Interference
Alternating Current Generator
Line Spectrum

And here is one of my writings.

Common Mistakes in Physics 1 - Acceleration Equations

Posted on 24 August 2014

I thought it might be useful for students if I write something about common mistakes. These are mistakes that many students make when they do physics questions. And the biggest problem is that no matter how many times I remind them, they would continue to make the same mistakes. So perhaps an article like this would help.

The mistake I want to talk about here is the most common one I have seen. It is about signs of quantities when using the acceleration equations. So when do we need to use these equations? Lets look at this example:


I throw a ball up. It leaves my hand with a speed of 6 m/s. It goes up and come down again. After 1 s, it is moving downwards with a speed of 4 m/s. What is the acceleration?

This is how I have seen many students do it:

The first acceleration equations is: a = (v - u)/t,

where v the final velocity is 4 m/s,

u the initial velocity is 6 m/s and

t the time taken is 1 s.

Substituting, they get a = (4 - 6) / 1 = - 2 m/s².

The correct answer should be 10 m/s², and they don't know why there is a minus sign.

So what went wrong?

The mistake is that they missed out the first two steps - two most basic and important steps. These two steps are not usually emphasised or mentioned in textbooks, notes or classes. So it is no wonder that many students missed them. But even with many reminders, I find that many students still forget these 2 steps.

So what are the 2 steps? Here they are:

  1. Choose a direction to be positive.

  2. Give signs to the vector quantities.

Why? Because acceleration and velocity are vectors, and vectors have directions. If we ignore this, we must surely get it wrong. Right?

So this is how I would do it:

Step 1

The motion is in the vertical direction. I can choose either up or down as positive. Either one is ok. I shall choose up as positive.

Step 2

To give signs:

initial u = +6 m/s (because ball is going up, and I have chosen up as positive);

final v = -4 m/s (because ball is going down - down is negative since I have chose up to be positive).

Therefore acceleration

a = (v - u) / t = [(-4) - (+6)] / 1 = - 10 m/s².

I get the correct number but why the negative sign?

If you remember, I have chosen up to be positive. This means that the sign tells us the direction. So a negative sign means downwards - i.e. the acceleration is downwards.

This makes sense since the force of gravity is pulling downwards on the ball.

And you must apply these 2 steps every time you use the acceleration equations.

Without exception.




PS. (1 November 2014)

When I explain this to students, one response I often get is - but my teacher never taught this. Or I have never seen this before. Or I don't believe this. Or (this is my favourite) my friend never told me this.

This may be so obvious to teachers (like 1 + 1 = 2) that they did not think they need to explain. Or teachers may focus on just teaching specific questions and steps that give the right answers.

As to why a student has not seen this before (or why their friends never told them), well what can I say?

I must say that my teachers never taught me either. What is worse - I have never in the past 40 years seen it mentioned in any textbook. Maybe this is one of the things that is either obvious or takes some time to explain. Even in the above article, I have only written out the steps but not the reasons.

If you are a physics student and you did not know about this, then I hope this explanation will be of some help.