Describing Motion

Two objects can start and finish at the same places but follow different paths. Distance records the path. Displacement compares only the final position with the initial position.

• Distance is the total length of the path travelled. It has no direction and cannot be negative.
• Displacement is the change in position in a stated direction. For a straight journey it is the directed line from the start to the finish.
• Walking 10 m north and then 10 m south gives a distance of 20 m and a displacement of zero. Returning to the start removes the displacement, but it does not remove the path already travelled.

distancedisplacementAB

Time turns distance into speed and displacement into velocity. This preserves the same scalar-vector pairing.

• Average speed uses the total distance travelled during the whole time interval. It has no direction.
• Velocity uses displacement, so its direction and sign matter.

• Average speed or velocity describes a time interval. An instantaneous value describes one moment, such as the speed shown by a speedometer.
• The instantaneous velocity will be obtained from the gradient of a displacement-time graph in the next lesson.

Velocity can change in magnitude, direction or both. Acceleration measures how quickly that velocity changes. It does not mean “moving fast”.

• Acceleration has unit m s⁻². An acceleration of 2.0 m s⁻² means that velocity changes by 2.0 m s⁻¹ each second.

• If velocity and acceleration point in the samedirection, speed increases. If they point in oppositedirections, speed decreases. Slowing down is also called deceleration.
• Zero velocity does not guarantee zero acceleration. A ball at the top of its flight has zero vertical velocity for one instant but still has acceleration $g$ downward.
• Zero acceleration does not guarantee zero velocity. An object can continue at constant non-zero velocity.