Mathematical equations are used to describe force and motion, work and energy, heat and temperature, and virtually every other topic in physics. Algebra is a basic technique in the physicist’s toolkit, used to rearrange the variables in an equation to solve for one variable.

Part 1: Using algebra to rearrange an expression

In this investigation, you will use algebra in a series of interactive simulations to solve for the desired variable. If you make a mistake, don’t worry: You can choose a different step to replace your previous answer. Look for the traffic lights along the way: A red light indicates that you should try again!

Open the first interactive element that asks you to solve the equation v = d / t for time t.

Choose the next step to solve the problem.

Inspect what happens algebraically to the expression because of your choice.

What was your solution to the algebra problem?

Did you solve the problem in the minimum number of steps?

In this interactive activity, you are given an algebraic problem: solve the equation v = d/t for time. In each step of the process, you have four choices of what to do next. You will have to complete one step correctly before starting the next step. Can you solve the problem in the minimum number of steps?

Part 2: Solve two more problems

Using the second interactive simulation, solve the algebraic equation x = x_{0} + v_{0}t for the initial speed v_{0}.

Using the third interactive simulation, solve the equation d = ½at^{2} for time t.

What was your solution for the second algebra problem?

What was your solution for the third algebra problem?

In this interactive algebra problem, you are to solve the algebraic equation x = x_{0} + v_{0}t for v_{0}. Can you solve the problem in the minimum number of steps?

In this interactive algebra problem, you are to solve the equation d = ½at^{2} for time. How many steps does it take you to solve it?