The kinetic energy (E) of an object, in joules, is found using the formula 𝐸=12𝑚𝑣2, where m is the mass in kg and v is the velocity of the object in m/s.

The kinetic energy (E) of an object, in joules, is found using the formula 𝐸=12𝑚𝑣2, where m is the mass in kg and v is the velocity of the object in m/s.

$E_{\text{kinetic}} = \frac{1}{2} m v^2.$

(a) Determine E when m = 2 kg and v = 1.2 m/s.

$\begin{array}{rcl} E &=& \frac{1}{2} \cdot m \cdot v^2 \qquad m = 2\ \mathrm{kg} \qquad v = 1.2\frac{\mathrm{m}}{\mathrm{s}}\\ E &=& \frac{1}{2} \cdot 2\ \mathrm{kg} \cdot (1.2\frac{\mathrm{m}}{\mathrm{s}})^2 \\ E &=& 1.2^2\ \frac{ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} \\ E &=& 1.44 \ \frac{ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} \\ \boxed{~ \begin{array}{rcl} \frac{ 1\ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} &=& 1\ J \end{array} ~}\\ \text{in joules }: \qquad E &=& 1.44 \ \ J \\ \end{array}$

(b) Determine m when E = 162 joules and v = 9 m/s.

$\begin{array}{rcl} E &=& \frac{1}{2} \cdot m \cdot v^2 \\ \frac{1}{2} \cdot m \cdot v^2 &=& E \\ m \cdot v^2 &=& 2 \cdot E \\ \mathbf {m} & \mathbf{=} & \mathbf{ \dfrac{ 2 \cdot E }{ v^2 }} \\ \boxed{~ \begin{array}{rcl} 1\ J &=& \frac{ 1\ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} \end{array} ~}\\ m & = & \dfrac{ 2 \cdot E }{ v^2 } \qquad E=162\ \mathrm{J}=162 \frac{ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} \qquad v = 9\frac{\mathrm{m}}{\mathrm{s}}\\ m & = & \dfrac{ 2 \cdot 162 \frac{ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} }{ (9\frac{\mathrm{m}}{\mathrm{s}})^2 } \\ m & = & \dfrac{ 324 \frac{ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} }{ 81\frac{\mathrm{m^2}}{\mathrm{s^2}} } \\ m & = & 4 \dfrac{ \mathrm{\mathrm{kg}\cdot m^2\cdot s^2}}{\mathrm{s^2\cdot m^2}} \\ m & = & 4 \ \mathrm{kg} \\ \end{array}$

Physics is SOOOO confusing!!!

(I've also been trying to learn some Physics today. )

http://web2.0calc.com/questions/heeeeeelp-got-test-tomorrow#r3

I am so confused.  I thought work was measured in Joules (I sorted that out earlier today) and now you are telling me that Energy is measured in Joules.  Is Work and Energy the same thing  ??????

ALSO

Your formula is NOT there   

Work is a form of energy transfer and so is measured in joules the same as energy.

The formula for kinetic energy is E = (1/2)m*v^2. Where E is energy, m is mass and v is velocity.

heureka beat me to it!

Yea that 12 and 2 had me baffled.  I knew no formulas had a 12 and a 2 in it like that.   LOL

Thank you Heureka and thank you Alan.  You are both wonderful.

It makes sense that work and energy transfer are the same thing and therefore both measured in Joules.

Thanks Alan. :))