Practice · Unlimited problems

Practice Lab

Fresh problems on everything in the module, as many as you like: positions, unit vectors, velocity, acceleration, guided paths, equations of motion and central forces. Each one comes with hints and a worked solution built from its own numbers, and once you have solved it you can see it in 3D.

Practice problems

Choose a topic, or Mixed for a bit of everything. Type your answer and press Check (or Enter). Stuck? Take a hint, or open the worked solution, then try another problem of the same kind.

Topic

Streak 0 Best 0 Solved 0

Problem code …

Figure P.1 The 3D view of the current problem: the point, force or motion it describes, with its velocity, acceleration and forces. It stays hidden until you solve the problem or open its solution, so it never gives the answer away. Then drag to rotate, and use Top and Front to check angles and heights.

Load a problem by its code

Every problem has a code such as cart2cyl-40718, shown above the problem and in the page address. The same code always gives the same problem, so you can send one to a classmate or your instructor, or come back to it later.

Problem code

Your progress

Your streak counts problems solved on the first try, in a row. Hints are fine. A wrong answer, or opening the solution before you answer, starts the streak again.

Problems by topic. Rate = first-try solves as a share of problems tried.
Topic	Tried	First try	Solved	Rate

Typing answers

Answer boxes understand math, so you can type exact values instead of hunting for decimals. Each box shows how it read your input (for example = 2.356), so you can catch a typo before you check.

What you can type
You type	It reads
`3pi/4` or `3π/4`	\(\tfrac{3\pi}{4} \approx 2.356\)
`135°` or `135 deg` (angle boxes)	\(135^\circ = \tfrac{3\pi}{4}\)
`2sqrt(3)` or `2√3`	\(2\sqrt{3} \approx 3.464\)
`sqrt(2)/2`	\(\tfrac{\sqrt{2}}{2} \approx 0.7071\)
`-3/2 + 2sqrt(3)`	\(-\tfrac{3}{2} + 2\sqrt{3} \approx 1.964\)
`2.83`	\(2.83\), a decimal: accepted when it is within about 1% of the exact value (for angles, within 0.01 rad)

Angles are compared modulo \(2\pi\), so \(\tfrac{7\pi}{4}\), \(-\tfrac{\pi}{4}\) and \(315^\circ\) all count as the same answer. A number with no unit in an angle box is read as radians. For a point on the \(z\)-axis (\(r = 0\)) any \(\theta\) is accepted.