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Speed and velocity

Forces and motion · level 4, lesson 2 of 6

A question to start

Two rovers drive at 4 cm/s. One heads north, the other south. Are they doing the same thing? And a toy train goes round a circular track at a steady speed. Is anything about its motion changing?

The idea

Speed says how fast. Velocity says how fast and which way. 4 cm/s is a speed; 4 cm/s north is a velocity.

That makes velocity something with a direction, like a force, and we draw it with an arrow. Two rovers at 4 cm/s, one going north and one south, have the same speed but opposite velocities.

The toy train on the circle keeps the same speed, but its direction keeps changing. So its velocity is changing all the time, even though its speed is not.

same speed,new direction

Velocities going opposite ways along a line can be written with signs: say east is positive, then 5 m/s east is \(+5\) m/s and 5 m/s west is \(-5\) m/s.

Why care? Because forces change velocity, not just speed. A force is needed to change how fast you go, or which way. That is why the next lessons say acceleration and turning both need a force.

Worked examples

1. A ball thrown up. At 10 m/s upwards, then at the top 0 m/s, then on the way down 10 m/s downwards. Same speed at start and end, opposite velocities.

2. A round trip. A rover drives 50 m east and then 50 m back west in 40 minutes. Its average speed is \(100 \text{ m} \div 40 \text{ min} = 2.5\) m/min. But it ended where it started, so its average velocity is zero.

Try it

  1. What is the difference between speed and velocity?
  2. A car drives round a roundabout at a steady 20 km/h. Is its velocity steady?
  3. With east as positive, write 3 m/s west as a velocity.
  4. A runner does one lap of a 400 m track in 80 s. What is her average speed? Her average velocity?
Answers
  1. Velocity is speed with a direction.
  2. No: its direction keeps changing.
  3. \(-3\) m/s.
  4. Average speed \(400 \div 80 = 5\) m/s. Average velocity zero: she ends where she began.

Common mistake

"Constant speed means constant velocity." Only in a straight line. Anything going round a curve at a steady speed has a changing velocity.

Where it leads