Velocity

At Heathrow airport, planes take off and land into the wind. When the wind blows from the west, arriving planes come in low over central London. When the wind swings round to blow from the east, the whole pattern flips, and the planes come in from the other side. The wind speed can be the same number on both days. What changed was a direction, and physics keeps a separate word for speed with a direction.

This one is video five of six in Units and describing motion, for combined science and triple physics students, Foundation or Higher. It stands on two before it: Distance and displacement, and Speed, typical speeds and s equals v t.

Velocity is speed in a stated direction. Its symbol is v, like speed, and its unit is metres per second, with a direction attached. Ten metres per second is a speed. Ten metres per second west is a velocity, because it says where the motion is heading. Speed is to velocity what distance is to displacement. Speed and distance are scalars. Velocity and displacement are the vectors, each carrying a direction. Which is a velocity: fifteen metres per second, fifteen metres north, or fifteen metres per second north? Fifteen metres per second north. It is the only option with both a per second and a direction. A velocity's direction can be given as a compass point, as a bearing, or as a sign against a direction you have called positive.

Take a lift. It rises at two metres per second, and later it comes down at two metres per second. Call upwards positive. Going up, its velocity is plus two metres per second. Now it comes down at the same two metres per second. What is its velocity? Minus two metres per second. The minus sign is not making it smaller. It is telling you the lift is going down, which a speed of two cannot. One exam board's specification lists this as a common mistake students make. They have a tendency to believe that a velocity must have a positive value and have difficulty in associating a reverse in direction with a change in sign. Put plainly, a reversal of direction is a change of sign, never a smaller number. The fix is to state your positive direction first, and then let the sign do the talking. A drone's velocity is plus eight metres per second. A minute later, its velocity is minus eight metres per second. Has the drone sped up, slowed down, or neither? Neither. The size stayed the same, and only the direction reversed. Drawn as arrows, the two velocities are the same length, pointing opposite ways. A velocity that changes like that will matter a great deal in the next chapter, on acceleration.

A tram runs one point two kilometres due north in two minutes, then comes straight back along the same track in three minutes. Start with the CONVERT line. One point two kilometres, arrow, one thousand two hundred metres. Two minutes, arrow, one hundred and twenty seconds. Three minutes, arrow, one hundred and eighty seconds. Leg one: v equals s over t, one thousand two hundred divided by one hundred and twenty. That is a speed of ten metres per second, and a velocity of ten metres per second north. Leg two: one thousand two hundred divided by one hundred and eighty is six point seven metres per second, to two significant figures. The velocity is six point seven metres per second south. Average speed for the whole trip is total distance over total time. Two thousand four hundred metres divided by three hundred seconds is eight metres per second. Average velocity uses the displacement instead. What is the tram's average velocity? Zero. The tram finishes where it started, so its displacement is zero, and so is its average velocity. It clearly moved, and its average speed says so. The average velocity only asks where it ended up, and the Distance and displacement video answers the same objection with a running track.

Someone writes that the velocity of a ball is twelve metres per second, and leaves it there. What is missing from that answer for the ball's velocity? A direction. As written it is only a speed, and up or down would both fit, which are opposite motions. Put the chapter's four quantities in a two-by-two picture. Distance and speed sit on the scalar side. Displacement and velocity sit beside them, on the vector side. Your handle for this video is that two-by-two picture: distance and speed tell you how far and how fast, and displacement and velocity add the direction.

Three new ones to check yourself on, and then you are done. Taking east as positive, a cyclist rides west at six metres per second. Her velocity? Minus six metres per second. West is the negative direction, and six is the speed. Now another. A lift goes up four floors and back down in a minute. Average velocity? Its average velocity is zero, because the lift is back where it started and its displacement is zero. Now a different one. Plus five, then minus five metres per second: faster, slower, or neither? Neither faster nor slower. The speed is five both times, and only the direction reversed. And the wind at Heathrow: the same speed on two different days can be two opposite velocities, and the planes follow the velocity.

Nailed it? A thumbs up marks this one as done, so the videos you have not thumbed are the ones left for later. If it still feels slippery, save it and come back; nobody gets the minus sign first time, and that is fine.

Next in the chapter: Measuring speed in the laboratory, where the numbers come from real equipment.

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