Scalar and vector quantities

1. Every physical quantity has a magnitude, which is its size given as a number with a unit, such as $40m$ or $12s$.
2. A scalar quantity has magnitude only, so a number and a unit describe it completely.
3. A vector quantity has magnitude and direction, so a number and a unit are not enough to describe it on their own.
4. Time, mass, distance and speed are scalars, because none of them involves a direction.
5. Displacement, velocity and force are vectors, because each one points or acts in a particular direction.
6. A vector can be drawn as an arrow, where the length of the arrow shows the magnitude and the way the arrow points shows the direction.
7. The direction of a vector can be given in words, such as north or down the ramp, or with a sign, where one direction is chosen as positive and the opposite direction is then negative.
8. Along a straight corridor, if movement to the right is taken as positive, then $+5m$ means $5m$ to the right and $-5m$ means $5m$ to the left.
9. A negative sign on a vector shows direction only, so it does not mean that the quantity is smaller than zero in size.

Distance and displacement

1. Distance is a scalar that measures the full length of the route travelled, including every bend and every change of direction.
2. Displacement is a vector that measures how far an object ends up from its starting point in a straight line, together with the direction.
3. Distance depends on the route taken, while displacement depends only on the start and finish positions.
4. Distance can only increase or stay the same during a journey, while displacement can increase, decrease or return to zero.
5. For a journey along a straight line with no change of direction, the distance and the magnitude of the displacement are equal.
6. For example, a pupil who walks $30m$ east along a corridor and then $10m$ back west has travelled a distance of $40m$ but has a displacement of $20m$ east.
7. A runner who completes one full lap of a $400m$ track has travelled a distance of $400m$ but has a displacement of zero, because the finish point is the start point.

Speed and velocity

1. Speed is a scalar that tells you how fast an object is moving, whatever its direction.
2. Velocity is a vector that gives the speed together with the direction of travel, such as $15m/s$ north.
3. Speed is worked out from the distance travelled, while velocity is worked out from the displacement.
4. Two cars travelling at $20m/s$ in opposite directions along the same road have the same speed but different velocities.
5. If one direction along the road is taken as positive, the velocities of the two cars are $+20m/s$ and $-20m/s$.
6. An object's velocity changes whenever its speed changes, its direction changes, or both change.
7. A car driving round a roundabout at a steady $8m/s$ has a constant speed but a changing velocity, because its direction keeps changing.
8. A tennis ball that is hit straight back at the same speed it arrived has an unchanged speed but a reversed velocity, so the sign of its velocity has changed.
9. A negative velocity means the object is moving in the negative direction, and it does not mean that the object is slowing down or moving slowly.