← Speed and velocity; scalars and vectors

Instantaneous velocity: the velocity right now

Which division gives a trip's average velocity?

A road trip's average velocity works out to 20 m/s north. Yet the car spent the trip crawling through towns and rushing down highways. Was it ever actually moving at 20 m/s?

You've already seen that an average velocity smooths a whole interval into one value. Sometimes you want something different: the velocity right now.

The velocity an object has at one single moment is its instantaneous velocity, as opposed to an average over an interval.

a value for a stretch, a value for a momentstartfinishone moment: an instantaneous velocitythe whole trip: one average velocity

A car's speedometer shows how fast the car is moving at this moment. That reading, together with the direction the car is traveling, is an instantaneous velocity.

A car's speedometer reads 55 mph. What extra information turns the reading into the car's instantaneous velocity?

'Instantaneous' does not mean brief or sudden. It means 'at an instant': the value belongs to one moment in time.

A radar gun clocks a pitched ball at 89 mph toward home plate at the moment it leaves the pitcher's hand. The value belongs to one moment, and it gives how fast and in which direction at that moment. That clocked value, together with its direction toward home plate, is an instantaneous velocity.

At exactly 2:00 pm, a harbor sensor logs the tidal current at 3 m/s flowing toward the sea. Which kind of quantity has the sensor logged?

Two pieces of information make up any instantaneous velocity: how fast the object is moving at that moment, and in which direction it is moving at that moment.

Your turn

Which measurement, by itself, comes closest to stating an instantaneous velocity?

Halfway through a journey, a driver's speedometer-plus-compass reading disagrees with the value the trip computer later reports as the journey's average velocity. Why can both be right?

A physics report must state a falcon's instantaneous velocity at the moment it crossed a survey line. Which entry is complete and correct in kind?