← Speed and velocity; scalars and vectors

Pick the quantity for the job: scalar or vector

Quantity 1: velocity. Quantity 2: speed. Classify each as a scalar or a vector.

You've already sorted the motion quantities into scalars and vectors. That sorted list matters when you pick a quantity for a real job: some jobs need a direction, and some do not.

Ask what the job's answer depends on: does direction matter to it? If the job is 'where will it end up?' or 'which way should it go?', a size alone cannot answer, so the job needs a vector. If the job needs only an amount, a scalar does the job.

Take one hiker on one walk, and vary the job. Predicting where she ends up depends on which way she walks: that job needs a vector, her velocity. Logging how much trail she covered needs only an amount: a scalar, her distance. Stating her pace needs only an amount too: a scalar, her speed.

one hiker, one walk: the job picks the quantitythe jobdoes direction matter?the quantitypredict where she ends upyesher velocity: a vectorlog the trail coverednoher distance: a scalarstate her pace: 8 km in 4 hnoher speed: a scalar

An air-traffic controller must predict where a plane will be in five minutes. Which quantity about the plane's motion does the job need?

A courier charges for a delivery ride by the kilometer ridden. The charge depends only on how much path was ridden; direction never enters the price. An amount alone is enough, so a scalar does the job: the distance.

A fitness app must record how much ground a runner covered, whatever route she took. Which quantity should the app record?

A rescue coordinator must tell a helicopter where a drifting life raft will be in one hour. The predicted position depends on how fast the raft drifts and on which way it drifts. Direction matters, so the job needs a vector: the raft's velocity.

A ship's navigator must decide which way to point the bow to reach a lighthouse. Which quantity does the job need?

Your turn

A student finds where a wandering robot ended up by reading its odometer: 'it drove 26 m, so it is 26 m from the start.' Which quantity did the job actually need?

For which job is a scalar all you need?

Job 1: reporting how much rope a winch has paid out. Job 2: reporting where a probe sits relative to its lander. Which kind of quantity does each job need?