”Mathematics is the language of physics”

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

Examples: Solve 𝑠= 𝑢−𝑣 2 𝑡 for u v t s= u−v 2 t |/𝑡 𝑠 𝑡 = 𝑢−𝑣 2 |∙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 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

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

Problems: Solve 𝐹=𝑚𝑎 for Solve 𝐸 𝑘 = 1 2 𝑚 𝑣 2 for a Solve 𝐸 𝑘 = 1 2 𝑚 𝑣 2 for v Solve 1 2 𝑚 𝑣 2 =𝑚𝑔ℎ for h

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

Rules for Significant Figures

Rules for Calculating with Significant Figures