**Work Done, Kinetic Energy (KE), Gravitational Potential Energy (GPE) and Power are all SCALAR quantities.**

Many have asked if Work Done is scalar or vector? Though from our textbook, **Work Done = Force x distance in the direction of the forc**e.

In other words, **Work Done = Force x Displacement**

We already know that **Force is a vector**. Weight being a force, is also a vector quantity. Displacement is distance in a specific direction, hence it is a vector quantity too. In tertiary education, you will learn in details that the **product (multiplication) of two vectors will result in a scalar or dot product**.

Since it is out of syllabus, it will be good to use other ways to help you to understand and recall.

Method 1 Remember vector x vector will end up a scalar. Similar to (-)x(-) = (+) Method 2 Consider moving a box up to a certain height, work done or gain in GPE is constant regardless of the path it takes (diagonal or vertical). Hence direction is not important, therefore **GPE is a scalar**.

When considering KE, since **KE = 1/2mv**^{2} , similar to Method 1, v^{2} is actually velocity x velocity. Hence it product of 2 vectors, resulting in **KE being a scalar**.

**Power = Energy Conversion/ time** or **Work Done / time**,

since energy, work done and time are scalar, **Power is a scalar quantity**.

**Other important note:** Power = Rate of work done = Rate of energy conversion.

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November 14, 2014 at 8:48 PM

what do we mean by 4D quantity?

I have searched but I am not clear if energy is scalar or vector.so pls would you solve my doubt.

thanks for giving your valuable time.

Manish prasad

class9

Delhi public school harni

Gujarat

India

November 14, 2014 at 9:30 PM

Hi manish! Energy is scalar. So kinetic energy, gravitational potential energy and work done are considered scalar quantities. Thank you

November 30, 2015 at 7:04 PM

Energy is a scalar quantity.Now you were asked to fetch water nobody wants to know the direction of the water flowing from the tap. All they want is the water you fetch .