D = ( R) D = distance covered in m V = velocity of the car in km/h (speed) R = road surface index
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1 GENERAL MATHEMATICS 3 WEEK 4 NOTES TERM 1 Being a good driver involves more than just knowing how to put petrol in the car and checking the tyre pressure. Good drivers are aware of the distance it takes their car to stop, their reaction time and the effect alcohol has on their judgement and reaction time. The distance required to stop a car is a combination of the distance the car travels during the driver s reaction time and the distance the car travels after the brakes have been applied. A formula can be used to calculate the distance required for a car to stop at different speeds on different road surfaces. The number of metres, D, required for the average driver to stop a car can be calculated by D = ( R) D = distance covered in m V = velocity of the car in km/h (speed) R = road surface index Exercise Set 1 Q1. Nina is travelling at a speed of 80 km/h on a gravel road. How far will it take her to stop?
2 Q2. Anthony is driving on a dry asphalt road at 60 km/h. a) What distance does his car travel after he decides to stop? b) How much further would it take him to stop on a wet asphalt road at 60 km/h? c) What advice would you give Anthony if it starts to rain while he is driving on an asphalt road? Q3. While André is driving at 50 km/h on a dry asphalt road, a young child runs onto the road 18 m in front of him. a) Will André be able to stop in time? Give a reason for your answer. b) Would the outcome be different if it was raining? (use a calculation to help). Q4. Yuvraj likes to go to the snow. a) How many metres will it take him to stop his car at a speed of 60 km/h on hard snow? b) Yuvraj drives slowly on the road near the ski lodge because the road is covered with ice. How many metres will it take him to stop at 15 km/h on the ice? c) Why do you think drivers are required to carry chains for their wheels in snow areas?
3 Q5. Mikhail s family often go for country drives. In dry weather, on an asphalt road, Mikhail s father usually drives at 100 km/h. What is a safe distance for Mikhail s father to leave between his car and the car in front of him? Give a reason for your answer. Q6. The maximum speed, V, in km/h, at which a car can travel before stopping within acertain distance, D, in metres, can be found by the formula V = 1000D R D = stopping distance in (m) R = road surface index When she is travelling on country roads, Lisa likes to allow herself 32 m to stop. What is the maximum speed Lisa can travel on a gravel road? In the previous questions you calculated average stopping distances based on an average driver s reaction time of 0 75 seconds. A driver s reaction time is the amount of time it takes for a driver to register the need to do something and begin to take action. Exercise Set 3 In all these questions t = 0.75 Q1. The distance, D, in metres, a car travels during the driver s reaction time (remember that this is the distance the car travels before the brakes are applied) can be found using the formula D = 5 v t 18 V the car s velocity or speed in km/h t the driver s reaction time in seconds
4 Calculate the reaction distances of an average driver at these speeds. a) 50 km/h b) 60 km/h c) 100 km/h d) 120 km/h Q2. The total distance, D, in metres, it takes to stop a car at different speeds on a dry asphalt road can be found by using the formula D = 5 v t 18 + (5t ) V = the car s velocity or speed in km/h t = the driver s reaction time in seconds a) When driving on a dry asphalt road at 60 km/h, what is a car s stopping distance? b) A special speed limit of 40 km/h applies to most roads near schools. How much shorter is the stopping distance on dry asphalt at 40 km/h than at 60 km/h? c) Why do you think this special school zone speed limit is necessary?
5 Statistics show that people who have been drinking significantly increase their risk of being involved in a traffic accident. It is against the law to drive a car if you have a blood alcohol concentration greater than The formula below can be used to determine the blood alcohol concentration BAC N A N number of drinks A volume of alcohol (in ml) in each drink Use this formula to answer the questions in Exercise Set 4. Exercise Set 4 Q1. A bottle of red wine contains 11% alcohol. Calculate the number of millilitres of alcohol in each of these glasses of the red wine. a) 150 ml b) 200 ml Q2. Wendy likes a wine that contains 9 5% alcohol. a) How many millilitres of alcohol are in a 150 ml glass of this wine? b) Use the formula BAC = N A to calculate Wendy s blood alcohol concentration after she has had three glasses of this wine. Q3. A bottle of whisky contains 35% alcohol. a) Calculate Theo s blood alcohol concentration after he has drunk three glasses, each containing 75 ml of whisky. b) The legal blood alcohol concentration for experienced drivers is Theo is an experienced driver. Can he drive legally after having these three drinks?
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