Speed, typical speeds and s = vt

In a thunderstorm you see the flash first. The thunder arrives afterwards, sometimes several seconds later, though both started at the same instant. Light crosses that gap almost instantly. Sound crosses it at about three hundred and thirty metres every second. So the wait for the thunder is a distance measurement you can make standing in a doorway.

Here is video four of six in Units and describing motion, and it serves combined science and triple physics students, Foundation and Higher equally. If the conversions feel rusty, Units, prefixes and standard form in physics is the one to revisit first.

Speed is the distance something covers in each unit of time. Its symbol is v, and its unit is metres per second. Three hundred and thirty metres per second means three hundred and thirty metres covered in every single second. Distance travelled equals speed times time. In symbols, s equals v t. Here s is the distance in metres, v is the speed in metres per second, and t is the time in seconds. It works because speed counts metres in each second. Multiply by the number of seconds, and you have counted every metre travelled.

Some questions give you no speed at all. They expect you to know a few. Walking is about one and a half metres per second. Running is about three metres per second. Cycling is about six metres per second. Sound in air is about three hundred and thirty metres per second. For vehicles, the size matters more than the exact value. A car on a main road does roughly thirteen to thirty metres per second, a fast train around fifty, and an airliner around two hundred and fifty. Wind is the odd one out. Its speed changes from hour to hour, so there is no single value to learn. Back to the storm, and this time the question gives you nothing to work with except your own memory. Six seconds from flash to thunder. Roughly how far away was the strike? About two kilometres. The sound covered three hundred and thirty metres in each of those seconds. In steps: s equals v t. Three hundred and thirty times six is one thousand nine hundred and eighty metres, which is about two kilometres. The typical speed carried the whole calculation.

Most questions need the equation turned round before anything goes in. So every calculation here is written as a three-line stack. Line one is the equation as you recall it. Line two is the rearrangement, with the operation said out loud. Line three is the substitution, with every number already in SI. To find the speed, you want v on its own. s equals v t, so divide both sides by t. That gives v equals s divided by t. Now for time: t equals s times v, s over v, or v over s? t equals s over v. Dividing each side of s equals v t by v leaves t on its own. Your handle for this video is the three-line stack: the equation, the rearrangement said out loud, then the substitution in SI. Here it is on a full question. A cyclist covers four point five kilometres in twelve minutes. Find the average speed in metres per second. CONVERT line first. Distance: four point five kilometres, arrow, four thousand five hundred metres. Time: twelve minutes, arrow, twelve times sixty, which is seven hundred and twenty seconds. Line one: s equals v t. Line two: divide both sides by t, so v equals s divided by t. Line three: v equals four thousand five hundred metres divided by seven hundred and twenty seconds. That is six point two five metres per second. And six point two five sits right beside the typical cycling speed of about six. The typical speeds double as a check on your own answer.

Two runners train on a field. Runner A covers one hundred metres in twenty seconds. Runner B covers two hundred and forty metres in forty seconds. Which runner is faster, A or B? Commit to one. Runner B, even though B took longer. Divide each distance by its time. A: one hundred divided by twenty is five metres per second. B: two hundred and forty divided by forty is six metres per second. One examiner's report on a Foundation paper, about a question on runners' speeds, says this. Less able candidates compared the times of each runner but did not calculate speeds. Comparing times only works when the distances match, and here they did not. The fix is to divide every distance by its own time before you compare anything. A different runner does two hundred metres: the first hundred at five metres per second, and the second hundred at two point five. Someone averages the two speeds. Five plus two point five, divided by two, gives three point seven five metres per second. That answer is wrong. Why is three point seven five metres per second the wrong answer? The runner spends far longer on the slow half. Averaging the speeds treats both halves as equal times, and they are not. Average speed is total distance divided by total time. First hundred metres: t equals s over v, one hundred divided by five, which is twenty seconds. Second hundred metres: one hundred divided by two point five, which is forty seconds. Total time: twenty plus forty, sixty seconds. Average speed: two hundred metres divided by sixty seconds, which is three point three metres per second, to two significant figures.

A train travels at a steady forty-five metres per second for twenty minutes. The question wants the distance it covers. CONVERT line: twenty minutes, arrow, twenty times sixty, which is one thousand two hundred seconds. The speed is already in metres per second. The first line is s equals v t again. The second needs no rearranging, because s is already alone. The third: forty-five times one thousand two hundred, which is fifty-four thousand metres. Now the speed doubles, and the time stays the same. What happens to the distance, and why? It doubles. Twice the speed for the same time covers twice the ground, so the train goes twice as far. That is one hundred and eight thousand metres, and nothing had to be recalculated. Seeing the relationship is what an explain-why question is really asking for.

Three to finish on, and none of them has appeared in this video. Three point six kilometres in forty minutes: what speed, in metres per second? One point five metres per second, a typical walking pace. Three thousand six hundred metres divided by two thousand four hundred seconds. Now a why. Why is an average speed not the average of the two speeds? Because the object spends more time at the slower speed. Average speed is total distance over total time. Try one more, back to the storm. Thunder comes four seconds after the flash: how far? About thirteen hundred metres. Sound covers three hundred and thirty metres every second, and four lots of that is one thousand three hundred and twenty. So the wait between flash and thunder was never about the weather. It was s equals v t, waiting for a speed you now carry in your head.

If you own this one, a thumbs up records it, and the videos without a thumb become the ones worth your time later. If it has not settled, save it for now; the rest of this chapter keeps using the three-line stack, so it will come back round.

Next in the chapter: Velocity, where the direction finally joins the speed.

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