v-t graphs

diff --git a/physics/light-matter-ref.md b/physics/light-matter-ref.md
index 4d8debb621d1dbeb9698160e8e90a2294127002c..8e3435663aa4b3d18c4eb7b38bf9c524a2a97aff 100644 (file)
--- a/physics/light-matter-ref.md
+++ b/physics/light-matter-ref.md
@@ -7,7 +7,6 @@ linestretch: 0.9
 ---
 
 \pagenumbering{gobble}
 ---
 
 \pagenumbering{gobble}

-<!-- \usepackage{multicols} -->

 
 # Light and Matter
 
 
 # Light and Matter
 


@@ -78,7 +77,7 @@ $$\rho = {hf \over c} = {h \over \lambda} = mv, \quad E = \rho c$$
 
 <!-- ![](graphics/energy-levels.png) -->
 - $\Delta E = hf = {hc \over \lambda}$ between ground / excited state
 
 <!-- ![](graphics/energy-levels.png) -->
 - $\Delta E = hf = {hc \over \lambda}$ between ground / excited state

-- $E$ and $f$ of photon: $E_2 - E_1 = hf = hc$
+- $E$ and $f$ of photon: $E_2 - E_1 = hf = {hc \over \lambda}$

 - Ionisation energy - min $E$ required to remove e-
 - EMR is absorbed/emitted when $E_{\operatorname{K-in}}=\Delta E_{\operatorname{shells}}$ (i.e. $\lambda = {hc \over \Delta E_{\operatorname{shells}}}$)
 
 - Ionisation energy - min $E$ required to remove e-
 - EMR is absorbed/emitted when $E_{\operatorname{K-in}}=\Delta E_{\operatorname{shells}}$ (i.e. $\lambda = {hc \over \Delta E_{\operatorname{shells}}}$)
 

diff --git a/physics/light-matter-ref.pdf b/physics/light-matter-ref.pdf
index 2492c0a75675951fa435c45ccab8f2d7f6a20347..5591f6f0e0c7066dca22aa23a45689841e483b19 100644 (file)
Binary files a/physics/light-matter-ref.pdf and b/physics/light-matter-ref.pdf differ

diff --git a/spec/kinematics.md b/spec/kinematics.md
index 9755b0e08e33b5acb541780eacce2e29722e1320..74044078c09e92c5a54403afbab1f3b2f79f14ca 100644 (file)
--- a/spec/kinematics.md
+++ b/spec/kinematics.md
@@ -2,11 +2,11 @@
 
 $${dV \over dt} = {\operatorname{change in volume} \over \operatorname{respect to time}}$$
 
 
 $${dV \over dt} = {\operatorname{change in volume} \over \operatorname{respect to time}}$$
 

-**position $x$** - distance from origin or fixed point
-**displacement $s$** - change in position from starting point (vector)
-**velocity $v$** - change in position with respect to time
-**acceleration $a$** - change in velocity
-**speed** - magnitude of velocity
+**position $x$** - distance from origin or fixed point  
+**displacement $s$** - change in position from starting point (vector)  
+**velocity $v$** - change in position with respect to time  
+**acceleration $a$** - change in velocity  
+**speed** - magnitude of velocity  

 
 $$v_{\operatorname{avg}}={\Delta x \over \Delta t}={{x_2 - x_1} \over {t_2 - t_1}}$$
 $$\operatorname{speed}_{\operatorname{avg}}={\Delta v \over \Delta t}$$
 
 $$v_{\operatorname{avg}}={\Delta x \over \Delta t}={{x_2 - x_1} \over {t_2 - t_1}}$$
 $$\operatorname{speed}_{\operatorname{avg}}={\Delta v \over \Delta t}$$


@@ -18,4 +18,12 @@ $$\operatorname{speed}_{\operatorname{avg}}={\Delta v \over \Delta t}$$
 | $v=u+at$ | $s$ |
 | $s=ut + {1 \over 2} at^2$ | $v$ |
 | $v^2 = u^2 + 2as$ | $t$ |
 | $v=u+at$ | $s$ |
 | $s=ut + {1 \over 2} at^2$ | $v$ |
 | $v^2 = u^2 + 2as$ | $t$ |

-| $s= {1 \over 2}(u+v)t$ | $a$ |
\ No newline at end of file
+| $s= {1 \over 2}(u+v)t$ | $a$ |
+
+## Velocity-time graphs
+
+- area = displacement
+
+## Definite integrals
+
+$$\int_a^b f(x) \cdot dx = [F(x)]_a^b=F(b)-F(a)$$
\ No newline at end of file