A robot vacuum wanders a living room and shuts down 3 m west of the charging dock where it began. What is its displacement?
You've already worked with quantities of two kinds without naming them. A distance answers 'how far?' completely on its own. A displacement is not complete until a direction is attached. The complete-on-its-own kind gets its name here.
A quantity that is fully described by a size alone is called a scalar. A distance of 70 m needs no direction to be complete; a time of 25 s needs none either.
A stopwatch shows 85 s. Why is this measurement a scalar?
An oven timer runs for 600 s. Ask 'which way?' of 600 s: the question does not apply to a time. The size alone fully describes it, so '600 s' is complete. Time is a scalar.
A pedometer shows 5000 m walked today. Distance is the length of path covered, whichever way the walking went, so its size alone fully describes it. '5000 m' is complete. Distance is a scalar.
A hiker reports: 'I walked 12 km today.' A friend asks: 'Which way?' The hiker answers: 'That doesn't change what I said.' Why is the hiker right?
Quantity 1: the 90 s a song lasts. Quantity 2: a chess piece's displacement, two squares toward the opponent. Which of the two is a scalar?
Which of these four is a scalar?
A student says: '70 m is a scalar when it measures the distance walked, but 70 m is not a complete description when it measures a displacement.' Is the student right?