Question

Given the formula E = 1/2mv², what are the units of E?​

Answer 1

E= Kinetic Energy there unit is joule(J)

Answer 2

`{\rm kg \cdot m^(2)\cdot s^(-2)}` (or equivalently,
`({\rm kg \cdot m^(2)}) / ({\rm s^(2)})`) assuming that
`m` stands for mass and
`v` stands for velocity.

Step-by-step explanation:

The standard unit for mass
`m` is
`{\rm kg}` (kilogram.)

The standard unit for velocity
`v` is
`{\rm m\cdot s^(-1)}` (meters per second, or equivalently
`({\rm m} / {\rm s})`.

Assume that
`m = 1\; {\rm kg}` while
`v = 1\; {\rm m\cdot s^(-1)}`. Apply dimensional analysis to find the unit of
`E`. In other words, multiply the units as if they were variables:

`\begin{aligned} E &= (1)/(2)\, m\, v^(2) \\ &= (1)/(2)\, (1\; {\rm kg})\, (1\; {\rm m\cdot s^(-1)})^(2) \\ &= (1)/(2)\, (1\; {\rm kg})\, (1\; {\rm m^(2)\cdot s^(-2)}) \\ &= (1)/(2)\; {\rm kg \cdot m^(2) \cdot s^(-2)} \\ &= (1)/(2)\, \frac{{\rm kg \cdot m^(2)}}{{\rm s^(-2)}}\end{aligned}`.

Hence, the unit of
`E` is supposed to be
`{\rm kg \cdot m^(2) \cdot s^(-2)}`.