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5.6.1c Velocity

5.6.1c Velocity

5.6.1c Velocity

Velocity

Definition

Velocity

Velocity is the speed of an object in a given direction.

  1. A car at 15 m/s15\ \text{m/s}15 m/s has a speed; a car at 15 m/s15\ \text{m/s}15 m/s east has a velocity, because both its speed and its direction are stated.
  2. Speed and velocity share units (such as m/s\text{m/s}m/s) but are different: speed is a scalar and velocity is a vector.
  3. Two objects can have the same speed but different velocities if they move equally fast in different directions.
  4. An object’s velocity also changes if its direction changes, even at constant speed, because direction is part of velocity.

Scalar and vector quantities

Definition

Scalar quantity

A scalar quantity has magnitude but no direction.

  1. The magnitude is the size or numerical value; a speed of 12 m/s12\ \text{m/s}12 m/s gives the magnitude but no direction.
  2. A vector quantity has both magnitude and direction; a velocity of 12 m/s12\ \text{m/s}12 m/s north gives the magnitude (12 m/s12\ \text{m/s}12 m/s) and the direction (north).
  3. Directions can be described using words such as north, south, left or right.

Applying the distinction to motion quantities

  1. Speed and distance are scalars (magnitude only).
  2. Velocity and displacement are vectors (magnitude and direction).
  3. Distance is the total path travelled; displacement is the straight-line change in position, in a stated direction.
    1. For a student who walks 5 m5\ \text{m}5 m east then 5 m5\ \text{m}5 m west, the distance is 10 m10\ \text{m}10 m but the displacement is 0 m0\ \text{m}0 m, because they finish at the start.
Exam technique
  1. Do not treat speed and velocity as identical: speed has no direction, velocity does.
  2. Do not confuse distance (total path) with displacement (straight-line change in position, with direction).
  3. To explain why a quantity is a vector, say it has both magnitude and direction.
  4. When comparing speed and velocity, make the contrast explicit: speed is a scalar with magnitude only, whereas velocity is a vector with magnitude and direction.
Self review
  1. What is velocity?
  2. What is the difference between a scalar and a vector?
  3. Which of speed, velocity, distance and displacement are scalars, and which are vectors?
  4. Can two objects have the same speed but different velocities?
  5. Why can distance differ from the magnitude of displacement?

5.6.1d Circular motion (HT)

Speed and velocity

Definition

Velocity

Velocity is speed in a given direction.

  1. Speed tells you only how quickly an object moves; velocity includes both the speed and the direction of motion.
  2. Two cars moving at the same speed but in different directions have different velocities.

Velocity during circular motion

  1. An object moving around a circle can travel at constant speed, covering equal distances in equal times.
  2. But its direction of motion changes continuously as it travels around the circle.
  3. Because velocity depends on direction as well as speed, the object’s velocity changes continuously.
Key Idea
  1. An object moving around a circle at constant speed has a constant speed.
  2. It has a continuously changing direction.
  3. It therefore has a continuously changing velocity.

A diagram showing an object moving in a circle of radius r. Velocity vectors v1 and v2 are shown tangential to the path at points P1 and P2, illustrating how the direction of velocity changes. The angular displacement Δθ and arc length Δs are also labelled.

Examples of circular motion

  1. A car on a roundabout at steady speed may move north at one point and west shortly after; its speed is unchanged, but its direction, and so its velocity, has changed.
  2. The same applies to a runner on a circular track, a seat on a Ferris wheel, a point on the edge of a rotating wheel, and an object in a circular orbit.
  3. At every point the object moves in a different direction from a moment earlier, so its velocity changes continuously.
Exam technique
  1. Do not assume constant speed means constant velocity; velocity is constant only when both the speed and the direction are unchanged.
  2. Do not write only “the car turns”; state that turning changes its direction, and therefore its velocity.
  3. Give the full chain: constant speed, changing direction, velocity is speed in a given direction, so the velocity changes.
  4. The key marking point is the change in direction; saying only “it moves in a circle” is not a complete explanation.
Self review
  1. What is the difference between speed and velocity?
  2. Can an object have constant speed but changing velocity?
  3. Why does an object’s direction change as it moves around a circle?
  4. Explain why a runner at constant speed on a circular track has changing velocity.
  5. What key word must be included when explaining changing velocity in circular motion?
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Velocity is the speed of an object in a given direction. For example, 15 m/s15 \, \text{m/s}15m/s describes speed, whereas 15 m/s15 \, \text{m/s}15m/s east describes velocity.

Speed is a scalar quantity because it has magnitude but no direction. Velocity is a vector quantity because it has both magnitude and direction.

Speed and velocity have the same units, such as m/s\text{m/s}m/s, but they are not the same quantity.

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What extra information distinguishes velocity from speed?

5.6.1c Velocity Revision Guide

  1. GCSE
  2. /Physics
  3. /5.6.1c Velocity