1. ”Mathematics is the language of physics”

2. Solving for a variable
We solve equations whith only symbols using exactly the same rules as for normal equations!

3. Examples: Solve 𝑠= 𝑢−𝑣 2 𝑡 for u v t
s= u−v 2 t |/𝑡 𝑠 𝑡 = 𝑢−𝑣 |∙2 2∙ 𝑠 𝑡 =𝑢−𝑣 |+𝑣 2∙ 𝑠 𝑡 +𝑣=𝑢
𝒖=𝟐∙ 𝒔 𝒕 +𝒗
s= u−v 2 t |/𝑡 𝑠 𝑡 = 𝑢−𝑣 |∙2 2∙ 𝑠 𝑡 =𝑢−𝑣 |−𝑢 2∙ 𝑠 𝑡 −𝑢=−𝑣 | ∙(−1)
−2∙ 𝑠 𝑡 +𝑢=𝑣 𝒗=𝒖− 𝟐𝒔 𝒕
s= u−v 2 t |∙2 2𝑠=(𝑢−𝑣)𝑡 |/(𝑢−𝑣) 2𝑠 𝑢−𝑣 =𝑡 𝒕= 𝟐𝒔 𝒖−𝒗

4. Solve 𝑣 2 = 𝑢 2 +2𝑎𝑠 for
u a s
𝑣 2 = 𝑢 2 +2𝑎𝑠 |−2𝑎𝑠 𝑣 2 −2𝑎𝑠= 𝑢 𝑢 2 = 𝑣 2 −2𝑎𝑠 | 𝑢= 𝑣 2 −2𝑎𝑠

5. Problems: Solve 𝐹=𝑚𝑎 for Solve 𝐸 𝑘 = 1 2 𝑚 𝑣 2 fora
Solve 𝐸 𝑘 = 1 2 𝑚 𝑣 2 for v
Solve 1 2 𝑚 𝑣 2 =𝑚𝑔ℎ for h

6. Physics problem solving algorithm
State starting values from the text
State your starting formulas
Solve for the variable of interest, if necessary combine several formulas
Enter numbers in the formula (with units)
Calculate and give the answer with unit and correct rounding
In IB we never write m/s, always m s-1!
same number of significant digits as the weakest link of the input

7. Rules for Significant Figures

8. Rules for Calculating with Significant Figures