Practice Questions on Speed and Distance with Solutions
Practice solving speed and distance problems with the provided solutions for scenarios involving a bullet, Bill jogging, and an airplane journey from New York to Los Angeles. Understand how to calculate speed, average speed, and arrival time based on distance and time measurements. Improve your arithmetic skills through these practical examples.
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CHAPTER 08 Arithmetic I Solutions: Practice Questions 5
08 Practice Questions 5 1. Find the speed of a bullet, which travels a distance of 30 metres in 2 5 seconds. Distance Time = Speed 30 2 5 = = 12 m/s
08 Practice Questions 5 2. Bill jogs a distance of 300 m. His motion is shown in the graph. Use the graph to find the speed at which Bill travelled during each of the three sections A, B and C. (i) A: 120 m in 60 s Speed =Distance =120 60 =2 m/s Time B: 220 120 = 100 m 160 60 = 100 s Speed =Distance =100 100=1 m/s Time
08 Practice Questions 5 2. Bill jogs a distance of 300 m. His motion is shown in the graph. Use the graph to find the speed at which Bill travelled during each of the three sections A, B and C. (i) C: 300 220 = 80 m 300 160 = 140 s Distance Time 80 140 4 0 571428 7 = Speed = = = 0 57 m/s =
08 Practice Questions 5 2. Bill jogs a distance of 300 m. His motion is shown in the graph. Can you suggest a reason why Bill s speed would have changed during the 300 m. (ii) Tiredness Gradient of the road getting steeper
08 Practice Questions 5 2. Bill jogs a distance of 300 m. His motion is shown in the graph. (iii) Find the average speed that Bill jogged at, over the full 300 m. Total distance Total time = Speed 300 300 = = 1 m/s
08 Practice Questions 5 3. An airplane leaves New York and travels 3,930 km to Los Angeles. The journey takes 4 hours 22 mins. Draw a distance/time graph to represent this information. (i) 22 60 22 mins hours = 0 36 h 0 37 = Time=4+0 37=4 37 h
08 Practice Questions 5 3. An airplane leaves New York and travels 3,930 km to Los Angeles. The journey takes 4 hours 22 mins. Hence, or otherwise, find the speed of the airplane. (ii) Distance Time 3930 4 37 900 km/h = Speed = =
08 Practice Questions 5 4. A train leaves Waterford at 10:25 and travels 165 km at an average speed of 75 km/h to Dublin. At what time does it arrive in Dublin? Distance Speed 165 75 2 2 h = = Time = 2 2 h 2 h 12 mins 10 h 25 m + 2 h 12 mins = 12:37 pm
08 Practice Questions 5 5. A person is travelling at 20 m/s for 4 hours and 20 minutes. Represent this information in a distance/time graph. (i) 20 m/s 60 = 1200 m/min 60 = 72,000 m/hr 1000 = 72 km/hr
08 Practice Questions 5 5. A person is travelling at 20 m/s for 4 hours and 20 minutes. (ii) How far did the person travel? Speed = 20 m/s Time = 4 hours and 20 minutes = ((4 60) + 20) 60 = 15600 seconds Distance = Speed Time = 20 15600 = 312000 m = 312 km
08 Practice Questions 5 6. Convert 12 metres per second (m/s) into: metres per hour (m/hr) (i) 1 hour = 3600 s (60 60) 12 3600 = 43200 m/hr kilometres per hour (km/h) (ii) 1 km = 1000 m 43200 1000 =43 2 km/hr
08 Practice Questions 5 7. Convert 72 km/h into: metres per hour (m/hr) (i) 1 km = 1000 m 72 1000 = 72000 m/hr metres per second (m/s) (ii) 1 hour = 3600 s 72000 3600 =20 m/s
08 Practice Questions 5 8. Light travels at a speed of approximately 2 9 108 m/s. How many kilometres will light travel in 12 minutes? Express your answer in the form a 10n, where n and 1 a < 10. 2 9 108 m/s 1 km = 1000 m 2 9 108 1000 =2 9 105km/s 12 mins = 12 60 s = 720 s Distance = Speed Time = 2 9 105 720 = 208800000 km = 2 088 108 km
08 Practice Questions 5 9. The time taken by Edel to travel from Derry to Waterford, a distance of 378 km, is six hours. Her return journey from Waterford to Derry, by the same route, takes an extra 45 minutes. Draw two distance/time graphs to represent Edel s journeys. (i)
08 Practice Questions 5 9. The time taken by Edel to travel from Derry to Waterford, a distance of 378 km, is 6 hours. Her return journey from Waterford to Derry, by the same route, takes an extra 45 minutes. By how many km/h is her average speed slower on the return journey? (ii) Speed =Distance Speed =Distance Time Time =378 =378 6 75 = 56 km/hr 6 = 63 km/hr 63 56 = 7 km/hr slower
08 Practice Questions 5 10. How many miles per hour is equivalent to a speed of 22 metres per second, given that 1 mile is equal to 1 6 km. 22 m/s 60 = 1320 m/min 1320 60 = 79200 m/hr 79200 1000 = 79 2 km/hr 1 mile/hr = 1 6 km/hr 79 2 1 6 =49 5 mile/hr
08 Practice Questions 5 11. A motorist drove 60 km on a motorway in 40 minutes. He drove the next 25 km on a side road in 35 minutes. Draw a distance/time graph to represent the motorist s journey. (i)
08 Practice Questions 5 11. A motorist drove 60 km on a motorway in 40 minutes. He drove the next 25 km on a side road in 35 minutes. Find his average speed in km/h. (ii) = Total distance 85 km = 1 25 hours = Total time 75 mins Speed =Distance =85 1 25=68 km/hr Time
08 Practice Questions 5 12. A train travelled the first 120 km of a journey in 1 hour and 12 minutes. It then travels the remaining 60 km in 48 minutes. Draw a distance/time graph to represent the train s journey. (i)
08 Practice Questions 5 12. A train travelled the first 120 km of a journey in 1 hour and 12 minutes. It then travels the remaining 60 km in 48 minutes. Find the average speed of the train for the whole journey (ii) = Total distance 180 km = = Total time 120 mins 2 hrs Distance Time 180 2 90 km/hr = Speed = =
08 Practice Questions 5 13. George frequently travels from his home to Galway, a distance of 119 km. The journey usually takes 1 hour 45 minutes. Find his average speed in kilometres per hour for the journey. (i) Distance=119 km Time=1 hr 45 mins=1 75 hrs Distance Time 119 1 75 = = = Speed 68 km/hr
08 Practice Questions 5 13. George frequently travels from his home to Galway, a distance of 119 km. The journey usually takes 1 hour 45 minutes. On a day of very heavy rain his average speed on a 28 km section of the journey was reduced to 35 km/h. How long did this section of the journey take on that day? (ii) Distance=28 km Speed=35 km/hr Time=Distance =28 35=0 8 hr Speed =48 mins
08 Practice Questions 5 13. George frequently travels from his home to Galway, a distance of 119 km. The journey usually takes 1 hour 45 minutes. (iii) How much longer did the total journey take on that day, if he completed the rest of the journey at his usual average speed? Give your answer correct to the nearest minute. Speed=68 km/hr = 119 28 = Distance 91 km Distance Speed 91 68 = = 1 338 hrs = Time Total time on wet day = 0 8 + 1 338 = 2 138 h Time difference = 2 138 1 75 h = 0 388 hours ( 60) = 23 28 min = 23 minutes
08 Practice Questions 5 14. Two athletes running towards each other at 4 m/s and 6 m/s are 750 m apart. How long will it take them to meet? First runner: Second runner: Distance = Speed Time Distance = Speed Time = 6 x t = 4 x t = 6t = 4t Distance travelled by 1st + distance travelled by 2nd = 750 m 4t + 6t = 750 m 10t = 750 t = 75 s
08 Practice Questions 5 15. A car travelling at 85 km/h is 550 m behind another car travelling at 60 km/h in the same direction. How long will it take the first car to catch the second car? Distance travelled by faster train = Distance travelled by slower train + 550 m 85t = 60t + 0 55 85t 60t = 0 55 25t =0 55 t =0 022 hr =1 min 19 s =79 s
08 Practice Questions 5 16. A train of length 110 metres approaches a tunnel of length 425 metres. If the train is travelling at 72 km/h, how long will it take it to pass completely through the tunnel? Give your answer correct to the nearest second. Tunnel + train length 425 + 110 = 535 m 72 km/hr = 72 000 m/hr Distance Speed 535 72000 = = 0 00743 hr = Time =0 4458 min =26 75 s =27 s
08 Practice Questions 5 17. The distance from town A to town B is half the distance from town B to town C. The total journey from town A to town C, through town B, is 120 km. A car travels at ? km/h from town A to town B. It increases its speed by 20 km/h on the journey from town B to town C. The total time for the journey is 1 hr 18 minutes. Find the distance from town A to town B. (i) AB=1 2BC B divides [AC] in 1:2 AB =1 3| AC | =1 3(120) =40 km
08 Practice Questions 5 17. The distance from town A to town B is half the distance from town B to town C. The total journey from town A to town C, through town B, is 120 km. A car travels at ? km/h from town A to town B. It increases its speed by 20 km/h on the journey from town B to town C. The total time for the journey is 1 hr 18 minutes. Find the time taken for the car to travel from town A to town B, in terms of x. (ii) Time=Distance =40 Speed x
08 Practice Questions 5 17. (iii) Find the value of x. Distance from B to C = 80 km Speed from B to C = x + 20 80 Time to go from B to C = x+ 20 18 60 Time from A to B Time from B to C 1 3 + = + 1 h hr 40 x 80 + + 1 3 = 20 x We must now solve this equation.
08 Practice Questions 5 17. (iii) Find the value of x. 40 x 80 + + 1 3 = 20 x 40(x + 20)(1) + 80(x)(1) = 13(x)(x + 20) 40x + 800 + 80x = 13x2 + 26x 0 = 1 3x2 94x 800 ( 10) 0 = 13x2 940x 8000 (factorise) 0 = (13x + 100) (x 80) 13x + 100 = 0 x 80 = 0 13x = 100 x =-100 x = 80 13 x cannot be negative, therefore x = 80 km/hr.
08 Practice Questions 5 17. Dublin s port tunnel has a length of 4 5 km and runs from Dublin port to the M50 motorway. The speed limit, while inside the tunnel, is 80 km/h. A traffic management system records the time a vehicle enters and exits the tunnel. It then uses these times to determine whether the vehicle has broken the speed limit. The entry and exit times for three vehicles A, B and C, are recorded in the following table. Note that each record gives the time in hours, minutes and seconds, to the nearest second. Vehicle A B C Time of entry 09:12:22 11:58:42 17:08:23 Time of exit 09:16:05 12:01:47 17:11:42
08 Practice Questions 5 17. Dublin s port tunnel has a length of 4 5 km and runs from Dublin port to the M50 motorway. The speed limit, while inside the tunnel, is 80 km/h. The entry and exit times for three vehicles A, B and C, are recorded in the table. Note that each record gives the time in hours, minutes and seconds, to the nearest second. A 3 min 43 s 0 06194 hr (i) Did any of these vehicles break the speed limit? 4 5 0 062=72 65 km/hr Speed =Distance = If yes, which one(s)? Justify your answer. Time B 3 min 5 s 0 05138 hr Speed =Distance Time Where appropriate, give calculations to two decimal places. 4 5 0 051=87 57 km/hr = Vehicle A B C Time of entry Time of exit 09:12:22 11:58:42 17:08:23 C 3 min 19 s 0 05527 hr Speed =Distance Time 09:16:05 12:01:47 17:11:42 4 5 0 055=81 41 km/hr = B and C are above the speed limit of 80 km/hr.
08 Practice Questions 5 17. Dublin s port tunnel has a length of 4 5 km and runs from Dublin port to the M50 motorway. The speed limit, while inside the tunnel, is 80 km/h. The entry and exit times for three vehicles A, B and C, are recorded in the table. Note that each record gives the time in hours, minutes and seconds, to the nearest second. 80 1 025 = 82 km/hr (ii) To allow for variations in speedometers, the roads authority allows a tolerance of 2 5% to the 80 km/h speed limit. This means that a vehicle will not receive a speeding fine unless its speed is outside of the tolerance. B is still outside the speed limit, including tolerance, of 82 km/hr. Vehicle A B C Time of entry Time of exit 09:12:22 11:58:42 17:08:23 your answer. Taking the tolerance into account, will any of these vehicles get a speeding fine? If yes, which one(s)? Justify 09:16:05 12:01:47 17:11:42
