Velocity at one instant

The idea

The average velocity over a large time interval may differ from the velocity at a particular instant; the term velocity means the velocity of an object at a particular instant.

Same place, different moment

An athlete runs from O to A and then back towards B. She is at the same point of the track on the way out and on the way back.

Do you think her velocity is the same on the way out and on the way back?

• No, the direction of her motion is different
• Yes, because she is at the same point
• Yes, because her speed stays the same

Three views

Open each tab and read the velocity.

An instant and an interval

Taking her to run steadily, the velocities at 6 s and at 14 s were +10 m s⁻¹ and −10 m s⁻¹, while the average velocity over the long interval from 0 s to 16 s was +2.5 m s⁻¹. A long-interval average hides what happens at each moment. From now on, when the book says velocity, it means the velocity at a particular instant.

The average velocity over a large time interval may differ from the velocity at a particular instant. In this chapter the term velocity means the velocity of an object at a particular instant.

Notes

Velocity here means the velocity at a particular instant. The average over a large interval may differ from it.

Check yourself

In this chapter, the word velocity means the velocity of an object…

An athlete's displacement is 40 m in 16 s. What is her average velocity over this interval?

Answer: 2.5 m s⁻¹

40 m ÷ 16 s = 2.5 m s⁻¹.

At 14 s the athlete's velocity is −10 m s⁻¹, but her average velocity from 0 s to 16 s is +2.5 m s⁻¹. What does this show?

The reading of a vehicle's speedometer is nearly the same as…

• over a large time interval. The velocity over a time interval is called the average velocity. Velocity means the value at a particular instant.
• over the whole journey. That would be an average. Velocity here means the value at a particular instant.
• at a particular instant — correct. Yes!
• The average velocity over a large time interval can differ from the velocity at an instant — correct. Yes!
• One of the two numbers must be wrong. Both are right. They describe different things: one is at an instant and the other is over an interval.
• Velocity does not have a negative value. A minus sign shows the direction of the velocity, here towards the left, so a velocity can be negative.
• the average velocity over the whole journey. The speedometer shows a value for the present moment, not an average over the whole journey.
• the magnitude of the velocity at an instant — correct. Yes!
• the displacement of the vehicle. Displacement is measured in metres. The speedometer shows how fast the vehicle is moving.