Formula Test Drive: Which Rearrangement Works?

An educational simulation game. Choose a rearranged formula, check its units, and let a car show whether it really works.

Rearranging formulasChecking units

TEST TRACK

How long to the line?

Ready
Enable JavaScript to drive the car. The instructions and worked example remain readable.
Velocity vAcceleration aGoalYour formula
Your formula?

Time

0.00 s

t

Position

0.00 m

x

Velocity

0.00 m/s

vₓ

Acceleration

0.00 m/s²

aₓ

Your value

—

?

Pick a formula

Read the situation, then choose the rearrangement you think is right. The car will drive with the value it gives.

Pick the formula that really works.

Mission score—

The right formula earns 100 points. Choosing it on the first drive adds 50.

✓ Right formula① First try

How to play Formula Test Drive

  1. Choose a situation and read the given values and the unknown.
  2. Rearrange the formula yourself, or compare the four options.
  3. Turn on the units check: an option whose units do not match the unknown is wrong.
  4. Choose a formula and press Play. The car drives with the value it gives: it should end on the line or at the target speed.

Check a rearranged formula twice

After rearranging a formula, check it in two ways. First, the units: the right-hand side must have the units of the unknown. If t = v ÷ d, the units are (m/s) ÷ m = 1/s, not seconds, so the formula is wrong. Quantities with different units can never be added. Second, the meaning: some wrong formulas have the right units, like a = (v + v₀) ÷ t, so test them on a real situation or on a simple case you already know.

A focused learning model

Each situation has constant acceleration on each part of the motion, computed exactly from the chosen value. A run that would last longer than 8 s plays faster, and the speed-up is shown. The units shown with each formula are worked out from the units of the given quantities.

Changing language keeps your situation, choice, attempts, and drive.