18 Speed, Distance and Time, Study notes of Physics

Download 18 Speed, Distance and Time and more Study notes Physics in PDF only on Docsity! 18 18.1 Speed, Distance and Time Speed In this section we introduce the idea of speed, considering both instantaneous speed and average speed. Instantaneous speed speed at any instant in time distance travelled Average speed ———$§{_— time taken If a car travels 100 miles in 2 hours, 100 2 50 mph The car does not travel at a constant speed of 50 mph; its speed varies during the journey between 0 mph and, perhaps, 70 mph. The speed at any time is called the instantaneous speed. average speed The following table lists units in common use for speed and their abbreviations: Distance Time Speed Abbreviation mile hours miles per hour mph kilometres hours kilometres per hour km/h metres hours metres per hour m/h metres seconds metres per second m/s feet seconds feet per second f.p.s. or ft. per sec. centimetres seconds centimetres per cm/sec or cm/s second Example 1 Judith drives from Plymouth to Southampton, a distance of 160 miles, in 4 hours. She then drives from Southampton to London, a distance of 90 miles, in 1 hour and 30 minutes. Determine her average speed for each journey. 109 1 8 1 MEP Y8 Practice Book B E® Solution Plymouth to Southampton Average speed = “ = 40 mph Southampton to London Time taken = | hour and 30 minutes = it hours or 3 hours 2 2 8 . | Average speed 4 Example 2 John can type 960 words in 20 minutes. Calculate his typing speed in: (a) words per minute, (b) words per hour. E® Solution (a) Typing speed 960 20 48 words per minute (b) Typing speed = 48 x 60 2880 words per hour 110 MEP Y8 Practice Book B Example 2 Chris cycles at an average speed of 8 mph. If he cycles for 65 hours, how far does he travel? Solution Distance = speed x time = 8x ot 2 = 52miles Example 3 Nikki has to travel a total of 351 miles. She travels the first 216 miles in 4 hours. (a) Calculate her average speed for the first part of the journey. (b) Ifher average speed remains the same, calculate the total time for the complete journey. Solution distance (a) Average speed = time _ 216 4 = 54 mph (b) Time = distance speed _ 351 54 6.5 hours 113 18.2 MEP Y8 Practice Book B Exercises 1. Calculate the distance that you would travel if you drove for: (a) 3 hours at 20 mph (b) 8hours at 60 mph (c) 5 hour at 76 mph (d) 5 hours at 42 mph (e) 64 hours at 40 mph (f) 30 minutes at 33 mph (g) 45 minutes at 60 mph (h) 90 minutes at 45 mph How long does it take to travel: (a) 120 miles at 40 mph (b) 300 miles at 50 mph (c) 240 miles at 60 mph (d) 385 miles at 70 mph (e) 60 miles at 40 mph (f) 360 miles at 30 mph (g) 390 miles at 60 mph (h) 253 miles at 46 mph A car travels 300 miles in 5 hours. Calculate the average speed of the car in: (a) _ mph, (b) miles per minute. How long does it take for the car to travel 82 miles? Janet and Bill leave their home at the same time. Janet has 60 miles to travel and drives at 40 mph. Bill has 80 miles to travel and also drives at 40 mph. (a) How long does Janet's journey take? (b) How much longer does Bill spend driving than Janet? An athlete can run long distances at 4 metres per second. How far can she run in: (a) 50 seconds, (b) 3 minutes, (c) 1 hour, 1 d) 2—hours ? (d) 3 hou Andrew rows at an average speed of 2 metres per second. (a) How long does it take him to row: (i) 70m, (ii) 800m, (iii) 15 km? 114 18.3 10. MEP Y8 Practice Book B (b) How far can Andrew row in: (i) 12 seconds, (ii) 35 minutes, (iii) 4 hours ? A snail moves 5 m in 2 hours, If the snail moves at the same speed, calculate: (a) the time it takes to move 20 m, (b) _ the distance it would move in 35 hours, (c) the time it takes to moves | m, (d) _ the distance that it moves in 15 minutes. Laura drives for 3 hours at 44 mph. Clare drives 144 miles in 4 hours. (a) Who travels the greater distance? (b) Whose speed is the slower? (c) How far would Laura travel if she drove for 3 hours at the same speed as Clare? A lorry travels for 3 hours at 48 mph and then for 2 hours at 53 mph. (a) | What is the total distance travelled by the lorry? (b) What is the average speed for the whole journey? Sally drives for 2 hours at 50 mph, then drives 80 miles at 40 mph, and finally drives for 30 minutes at 60 mph. (a) Calculate the total distance that Sally drives. (b) Calculate the time that Sally takes for the journey. (c) Calculate her average speed for the whole journey. Problems with Mixed Units In this section we consider working with mixed units, and with changing units used for speeds. Example 1 (a) (b) Convert | hour 24 minutes to hours (decimal). Write 2.32 hours in hours and minutes. 115 18.3 MEP Y8 Practice Book B Exercises 1. Convert the following times from hours and minutes to hours, giving your answers as mixed numbers and decimals, correct to 2 decimal places. (a) 1 hour 40 minutes (b) 3 hours 10 minutes (c) 1 hour 6 minutes (d) 2 hours 18 minutes (e) 3 hours 5 minutes (f) 6 hours 2 minutes (g) Ll hour 7 minutes (h) 2 hours 23 minutes Change the following times to hours and minutes: (a) 1Z hours (b) 1.2 hours (c) 3.7 hours (d) 4.4 hours (e) 1.45 hours (f) 3.65 hours A car travels 60 miles in 50 minutes. Calculate the average speed of the car in mph. Jane drives 80 miles in 1 hour and 40 minutes. Calculate her average speed. Convert the following speeds to km/h: (a) 60 mph (b) 43 m/s (c) 66 m/s (d) 84 mph Convert the following speeds to mph: (a) 16 m/s (b) 82 km/h (c) 48 km/h (d) 7m/s Alec drives 162 km in 2 hours and 12 minutes. Calculate his average speed in: (a) km/h (b) m/s (c) mph Give your answers to 2 decimal places. Jai drives 297 miles in 5 hours and 24 minutes. (a) Calculate his average speed in mph. (b) He then drives for a further | hour and 28 minutes at the same average speed. How far has he travelled altogether? Give your answers to 2 decimal places. 118 18.4 MEP Y8 Practice Book B 9. A train travels at 40 m/s. Calculate the time it takes to travel: (a) 30000 m, (b) 50km, (c) 200 miles. 10. A long distance runner runs at an average speed of 7 mph. How long will it take the runner to run: (a) 20 miles, (b) 15 km, (c) 10000 m? Distance-Time Graphs Graphs that show distance against time can be used to describe journeys. The vertical scale shows the distance from the starting point or reference point. Travelling away from starting point at a constant speed Distance From Starting Point Returning to starting point at a constant speed Time The graph above illustrates 3 parts of a journey. The gradient of a straight line gives _ Distance the speed of the moving object. Gradient is a measure of the speed. Rise Note that a negative gradient indicates that the object is moving towards the Step Gradient = Ris? starting point rather than away from it. Time 119 18.4 MEP Y8 Practice Book B Example 1 The graph shows how far a child is from home. Distance} m (a) Describe how the child moves. (b) Calculate the speed of the child on each part of the journey. Solution (a) The first part of the graph shows the child moving away from home at a constant speed. The second (horizontal) part of the graph shows that the child remains in the same position. The third part of the graph shows the child returning to the starting point at a steady speed. (b) During the first stage the child travels 1000 m in 80 seconds. distance Speed > time 1000 80 = 12.5 m/s During the second stage the speed of the child is zero. 120 MEP Y8 Practice Book B (e) Tom travels 3000 m in 30 mins. Speed = distance time _ 3000 ~ 30 = 100 m/minute Exercises 1. The following graph illustrates how Jamil moves as he goes to the paper shop: Distance ey ey o Time (segonds) (a) How long does it take Jamil to cycle to the shop? (b) What distance does Jamil cycle to get to the shop? (c) Calculate the speed at which Jamil cycles to the shop. (d) How long does Jamil spend at the shop? (e) Calculate the speed at which Jamil cycles on his way home. 2. Ona journey, Vera ¢ — drives 200 miles in 4 hours ¢ — rests for 1 hour ¢ drives another 100 miles in 2 hours. Draw a distance-time graph for Vera's journey. 123 18.4 3. MEP Y8 Practice Book B Describe the 5 parts of the journey (labelled (a), (b), (c), (d) and (e)) represented by the following distance-time graph: Distance ime (hours) Ray walks 420 m from his house to a shop in 7 minutes. He spends 5 minutes at the shop and then walks home in 6 minutes. (a) Draw a distance-time graph for Ray's shopping trip. (b) Calculate the speed at which Ray walks on each part of the journey. Mary sprints 200 m in 30 seconds, rests for 45 seconds and then walks back in rs minutes to where she started the race. (a) Draw a distance-time graph for Mary. (b) Calculate the speed at which Mary runs. (c) Calculate the speed at which Mary walks. After morning school, Mike walks home from school to have his lunch. The distance-time graph on the next page describes his journey on one day, showing his distance from home. (a) How far is Mike's home from school? (b) How long does it take Mike to walk home? (c) At what speed does he walk on the way home? Give your answer in m/s. (d) How long does Mike spend at home? 124 MEP Y8 Practice Book B (e) At what speed does he walk back to school? Give your answer in m/s. School Home Helen cycles for 20 minutes at 5 m/s and then for a further 10 minutes at 4 mis. (a) How far does she cycle altogether? (b) Draw a distance-time graph for her ride. The distance-time graph shown is for a 3000 m cross-country race, run by Rachel and James. Distance m 125 18.5 MEP Y8 Practice Book B Exercises 1. Three boys play football for a school team. The numbers of goals scored and matches played are listed below: Number of Goals Scored — Number of Matches Played Tan 16 32 Ben 22 40 Sergio 9 20 (a) Who scores the most goals per match? (b) Who scores the least goals per match? Alison plays 20 games for her school hockey team and scores 18 goals. Each match lasts 90 minutes. Calculate her scoring rate in: (a) — goals per hour, (b) goals per minute, (c) goals per match. When playing football, Jai claims to be able, on average, to score a goal every 40 minutes. How many goals would you expect him to score in: (a) 90 minutes, (b) 1 hour, (c) 5 matches, (d) 40 matches ? It costs 96p to send an air mail letter of mass 40 grams to Africa, and 107p to send it to China. (a) Calculate the cost per gram for each destination. (b) If the same rates apply to a 50 gram letter, calculate the cost for each destination. A package of mass 80 grams costs 39p to post first class and 31p to post second class. Calculate the cost per gram for first and second class post. A taxi driver charges £3.20 for a 4 km journey. How much does he charge: (a) per km, (b) per metre ? 128 18.5 10. MEP Y8 Practice Book B A taxi service makes a fixed charge of £1.20 and then 78p per km. Calculate the cost for journeys of the following lengths: (a) Ikm (b) 2km (c) 45km (@) 10.5km Alexi buys a 20 m length of fabric for £18.60. (a) | What is the cost per m of the fabric? (b) What would be the cost of 9.2 m of the fabric? Five people work in a shop. The following table lists the hours worked and the total paid in one week: Hours Worked Total Paid Dee 8 £28.64 Nadina 12 £43.44 Lisa 42 £302.40 Mary 38 £136.80 Clare 35 £134.40 (a) Who is paid the most per hour? (b) Who is paid the /east per hour? A 5 litre tin of paint is used to paint a wall that measures 6.25 m by 4 m. Calculate the rate at which paint is applied to the wall, in: (a) litres per m?, (b) cm? per m’, (c) ml per cm’. 129