P3a(i) Speed You will learn about: www.PhysicsGCSE.co.uk P3a(i) Speed You will learn about: How to calculate average speed and know its unit How to measure speed How a speed camera works

Speed vs Average Speed www.PhysicsGCSE.co.uk Careful… m/h means metres per hour… Speed is simply a measure of how fast an object is travelling. Cars have speedometers that tell you the speed. This can be in kilometres per hour, km/h, or miles per hour, miles/h. The Motorway has a speed limit of 70 miles/hour. This means the car can legally cover 70 miles in one hour. You can see on the speedometer above that 70 miles/h is the same as 110 km/h. This means that the car would travel 110 kilometres in one hour. A car never travels at the same speed all the time. Traffic lights, speed limits and roundabouts force the driver to speed up or slow down. So we can work out the average speed of a car during its journey: Average speed = 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 with units metres per second, m/s, or kilometres per hour, km/h. A car completes a 300km road trip in 4 hours. A student takes 12 minutes to walk 1.4km to school Its average speed is 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 Their average speed is 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 = 300𝑘𝑚 4 ℎ𝑜𝑢𝑟𝑠 = 75 km/h = 1400 𝑚𝑒𝑡𝑟𝑒𝑠 720 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 = 1.94 m/s 1 km = 1000m so 1.4 km = 1400m 1 minute = 60 seconds so 12 minutes = 720 seconds

How do speed cameras work? www.PhysicsGCSE.co.uk This is a speed camera. It measures speed. The speed camera takes a photo when the car crosses the first line… … and the last line. It records the time taken between the two photographs. So, if the car crosses the first line at 10.02 and 15 seconds and then crosses the last line at 10.02 and 20 seconds then the camera knows it took 5 seconds to cross all the lines. There are the white lines on the road. The lines are usually 1.5 metres apart from one another but can be separated by any distance. In the UK we tend to use 1.5 m If there are 25 lines altogether then the total distance is 25 x 1.5m = 37.5m And we know that average speed is 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 = 37.5 𝑚 5 𝑠 = 7.5 m/s This is about 17 miles per hour so under the 30 mile/h speed limit

How is average speed measured? www.PhysicsGCSE.co.uk Average speed is usually measured over a much longer distance. However, the principle is still the same as with the speed camera system. A distance of 1 km is chosen. Cameras like these take a photo of the car’s numberplate at the beginning and at the end of the 1 km journey. Each image carries a date and time stamp so a computer can work out the car’s average speed between the two cameras. Average speed cameras are better than standard speed cameras because it means the driver needs to drive more safely over a longer period of time and distance.

Rules about average speed, distance and time www.PhysicsGCSE.co.uk Some Rules: Average speed = 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 This means that if the average speed of a car doubles then the time taken to complete the journey will be halved. Double the average speed = half the time taken If the average speed of a car doubles then the car would have travelled twice as far Double the average speed = Double the distance If the average speed of the car doubles for twice the time the car travels for then the car will travel four times as far Double the average speed AND double the time = Four times the distance Rules about Units: 1 km = 1000m 1 hour = 3600 seconds (60x60 = 3600) 108 km/h becomes 108,000 𝑚𝑒𝑡𝑟𝑒𝑠 3600 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 = 30 m/s To change km/h into m/s: x1000 then ÷ 3600 To change m/s into km/h: ÷ 1000 then x 3600 REMEMBER:

Instantaneous speed www.PhysicsGCSE.co.uk Instantaneous speed = speed at an instant The speed at a particular instance is called the instantaneous speed. Initial speed = u Final speed = v A racing car starts with a speed of u and accelerates uniformly to v then: the average speed = 𝑢+𝑣 2 Final and v start with the same sound so this is easy to remember… If we know the average speed of the racing car then we can also work out: The distance in a certain time using 𝑢+𝑣 𝑡 2 How long it takes to travel a certain distance using 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑠𝑝𝑒𝑒𝑑 or 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 1 2 𝑢+𝑣 𝑡 So, increasing the average speed REDUCES the time taken to travel a particular distance. Speed limits depend on the type of road (carriageway, motorway or outside a school) and whether the area is urban or rural.

Questions www.PhysicsGCSE.co.uk Arjan ran 100 metres in 11.6 seconds. Billie ran 150 metres in 14.6 seconds. Who was fastest? Jody flew an aeroplane over 1000 km. It took just 1.5 hours. Calculate his average speed. Why is it difficult (or impossible) to maintain a constant speed over a journey? Craig travels at a speed of 2 m/s. How long will it take him to move 60 m? The speed limit on motorways is 70 miles/h which is 112 km/h. If a driver drives 80 km in 45 minutes do they break the speed limit? A snail travels at a speed of 0.5 mm/s. How far does it go in one hour? A car reaches a speed of 85 km/h in 30 s starting from rest. How fast does it go?

Answers to Questions www.PhysicsGCSE.co.uk Arjan ran 100 metres in 11.6 seconds. Billie ran 150 metres in 14.6 seconds. Who was fastest? Arjan= 100m/11.6s = 8.62 m/s Billie = 150m/14.6s = 10.27 m/s Billie fastest Jody flew an aeroplane over 1000 km. It took just 1.5 hours. Calculate his average speed. 1000 km / 1.5 hours = 666.67 km/h or 1000,000m / 5,400s = 185m/s Why is it difficult (or impossible) to maintain a constant speed over a journey? Obstacles such as roundabouts, traffic lights and pedestrians coupled with whether the road is urban or rural prevents this. Craig travels at a speed of 2 m/s. How long will it take him to move 60 m? time = distance travelled / speed = 60m / 2m/s = 30s The speed limit on motorways is 70 miles/h which is 112 km/h. If a driver drives 80 km in 45 minutes do they break the speed limit? Speed = distance / time = 80km / 0.75 hour = 106.7 km/h so no the speed limit is not broken A snail travels at a speed of 0.5 mm/s. How far does it go in one hour? Distance = speed x time = 0.5mm x 3600s = 1800mm or 1.8m A car reaches a speed of 85 km/h in 30 s starting from rest. How far does it go? The distance in a certain time using 𝑢+𝑣 𝑡 2 we need to convert the units so they are the same thus km/h needs to be in m/s as time is in seconds and distance needed to work out will be in metres. 85km/h = 85x1000 then ÷3600 = 23.6m/s Using equation = 0𝑚/𝑠+23.6𝑚/𝑠 𝑥 30 2 = 354m