Forces and motion, Year 11: distance, speed and velocity

Displacement

提示It is the vector partner of distance.

为什么Distance is simply how far something has travelled along its path, with no direction: a scalar. This quantity ignores the route and looks only at the start and the finish, and it always comes with a direction, such as '300 m due north'.

Distance 400 m; displacement zero

提示One of the two only cares where she began and where she ended.

为什么Distance counts every metre of the path, so one lap is 400 m. Displacement is the straight line from start to finish, and those are the same place, so it is zero. This is the clearest case of the two quantities giving different answers for one journey.

50 m north

提示The second leg undoes part of the first.

为什么Along a straight line, movements in opposite directions subtract: 80 m north followed by 30 m south leaves you 80 − 30 metres north of the start. The distance walked is different: 80 + 30 = 110 m. A displacement needs its direction as well as its size.

direction

提示It is the extra piece of information that 'due north' adds to '5 km'.

为什么A scalar has size only. Saying you have walked 5 km tells nobody where you are now; to know that, they need the displacement, which carries the missing piece. The same split separates speed from velocity.

The distance — the displacement is the straight line from start to finish, which is shorter

提示One follows the route; the other cuts the corner.

为什么Distance follows the route, so it is 3 + 4 = 7 km. Displacement is the single straight line joining the start to the finish; a scale drawing shows it is 5 km long, pointing 53° north of east. The size of a displacement can equal the distance travelled, but can never be more than it.

720 m

提示Check the unit of the time before you multiply.

为什么Distance travelled = speed × time, or s = v t, with s in metres, v in metres per second and t in seconds. Two minutes is 120 s, so s = 6 × 120. AQA expects this equation to be recalled.

180

提示Put the distance into metres, then rearrange so that time stands alone.

为什么Starting from s = v t, the time is t = s ÷ v. The distance must match the speed's unit: 4.5 km = 4500 m, so t = 4500 ÷ 25. That is three minutes.

1.5; 3; 6

提示Each one is double the one before it.

为什么These are the values AQA expects pupils to recall. Real speeds vary with age, fitness, the ground and how far the person has to go, so they are typical figures, not exact ones. They are useful for checking whether a calculated answer is sensible.

330

提示It is a little over three hundred.

为什么Sound travels roughly a third of a kilometre every second in air. The exact figure changes with the temperature of the air, which is why some books quote 340 m/s; AQA's typical value is the one to use in its exams unless a question gives another.

About 30 m/s

提示A mile is roughly 1600 m and an hour is 3600 s.

为什么70 miles is about 112 000 m, and dividing by the 3600 seconds in an hour gives about 31 m/s. A handy rule is that a speed in mph is a little more than twice the same speed in m/s. Knowing rough values like this for cars, trains and aeroplanes is part of the specification.

fitness; terrain

提示Think about who the person is, and about the route in front of them.

为什么A fit adult on a flat road moves faster than a tired child on a steep, muddy path, and nobody keeps up a sprint for ten kilometres. This is why the walking, running and cycling speeds are given as typical values.

The car's speed kept changing during the journey

提示Think of junctions, traffic lights and open road.

为什么Hardly anything moves at one unchanging speed: a car slows for bends and stops at lights, then goes faster on clear road. Dividing the total distance by the total time gives the average, which hides all of those changes.

Velocity

提示Two cars can show the same reading on the dial yet differ in this, if one heads north and the other south.

为什么Speed says only how fast; this quantity says how fast and which way — '20 m/s due east'. It is a vector. Change either the speed or the direction and it has changed, which is why a car turning a corner at a steady speed is still changing it.

No — equal speeds, but opposite directions

提示Check what the two dials read, then check where each bonnet is pointing.

为什么Velocity is speed together with direction, so both parts must match before two velocities are the same. These cars would be written as 30 mph east and 30 mph west — the same size, pointing opposite ways.

accelerating; velocity; speed

提示Three different words: one for motion that is changing, one that includes which way, one that does not.

为什么One journey needs all three words. How fast is one idea, how fast and which way is a second, and how quickly either of those is changing is a third. Everyday speech blurs them; physics asks for the right one on purpose.

distance

提示It is what a car's mileometer adds up.

为什么Each vector describing motion has a scalar twin with the direction left out: velocity and speed, displacement and its partner. The scalar tells you how much; the vector tells you how much and which way.

The bus is changing direction

提示A speedometer reports only one of the two things that make up velocity.

为什么Acceleration is any change in velocity, and velocity includes which way you are heading. Moving in a circle, the speed can stay the same while the heading turns all the time, so the velocity is constantly changing — which is why you feel pushed sideways in your seat even though the dial is steady.