vault backup: 2025-09-03 13:37:38

education/physics/PHYS2210/Unit 1.md

@@ -17,5 +17,9 @@ $$ \bar{v} = \dfrac{\text{final position-initial position}}{\text{final time - i
 
 
 $$ v_{\text{instant}} = v = \lim_{\Delta t \to 0}\frac{\Delta x}{\Delta t} = \frac{dx}{dt}$$
-- $x(t)$ -> position as a function of time
-$a_{\text{instant}} = a = \frac{dv}{dt} = \frac{d}{dt}()
+- $x(t)$ -> **position** as a function of time
+- $v(t)$ -> **slope** of position-vs-time (derivative of $x(t)$)
+- $a(t)$ -> **slope** of velocity-vs-time (derivative of $v(t)$)
+# Acceleration
+To find the instantaneous acceleration, we can apply the formula:
+$$a_{\text{instant}} = a = \frac{dv}{dt} = \frac{d}{dt} \frac{dx}{dt} = \frac{d^2x}{dt^2}$$