section c stopping distances · 2018-09-10 · stopping distance = reaction distance + braking...

SENIOR VCAL NUMERACY INVESTIGATION

1

Stopping distances

A car does not stop the instant you decide to do so. Two factors control how far a car travels between you seeing a problem and the car coming to a halt. The first is called the reaction time – the time it takes for the driver to react and hit the brake pedal – and the second is the braking distance – the distance the car travels when the brakes are being applied. 1. Write down a formula for stopping distance.

Reaction time

Reaction time is the time between seeing and acting

Measuring reaction time

Visual-Foot Reaction Time Test In this activity you will measure and calculate your own reaction time. Place a table close to but not touching a wall. Position the chair on top of the table to simulate a driver’s seat. One student sits on the chair with their right foot on the wall, pretending that the wall is the accelerator in a car. Have a strong student hold the chair. Another student places a metre ruler on the wall 10cm to the left of the driver’s foot, in the position of the brake in a car. Line up the zero on the ruler with the ball of the foot. The student holding the ruler lets the ruler fall – do NOT say GO! When the driver sees the ruler falling, the right foot should be moved as quickly as possible off the accelerator and onto the ruler (brake).

2. Complete the test three times, recording the number of centimetres showing on the ruler.

Trial 1 Trial 2 Trial 3

3. Calculate your average reaction time and then your reaction time using !!"#

𝑠𝑒𝑐.

Average time Reaction time

4. Average driver’s reaction time is 0.75 seconds. How did your reaction time compare to this? Explain.

Simple reaction time is the measure of a fully prepared person waiting for a signal, and their reaction to the signal. This is what you measured in the above exercises. In the real world of driving, many things can distract or impair a driver.

5. List possible distractions to a driver.

6. Write at least 50 words explaining what tests occurred and how reaction time was affected.


2

Calculating reaction distance

As you have a good estimate of your personal reaction time, you can now find how far you have travelled in that time. There are a number of possible methods for doing this, however, we will use the following:

Method – use the following formula 185VtD =

where: D = the distance the car travels in metres V = the car’s velocity or speed in km/h t = the driver’s reaction time in seconds Example: If you are travelling at 30 km/hr and your reaction time is 0.5 seconds, then:

Step 1: 18

5.0305 ××=D

1875

= 167.4=

Step 2: Distance travelled is 4.167 metres, before you hit the brake pedal. 7. Use your personal reaction time & the above method to calculate your reaction distances

at each of the following speeds in the table below. (Remember, this is the distance covered before the car even begins to slow down!)

Speed (V) Reaction Distance

40

50

60

80

100

120

8. Is there a relationship between a driver’s speed and their reaction distance? Explain. Braking distance

Braking distance is the distance you travel after you have applied the brakes as the car slows to stop. On a good bitumen surface, with a car in perfect condition, it takes about 21 m to stop while travelling at 60 km/hr. This gets longer on wet roads or gravel surfaces.


3

We can calculate the effects of different road surfaces on braking distances using the following formula:

D = ( V ) × (210 + 97R) 1000

where: D = distance travelled in metres

V = speed in km/hr R = surface factor

9. Add the following extra columns to your table. Calculate the braking distances for each of

the speeds below using the above formula.

Speed (V) Reaction Distance

Dry asphalt Wet asphalt Gravel Snow Ice

40

50

60

80

100

120

Surface factor Dry asphalt 1.4

Wet asphalt 1.7

Gravel 2.1

Hard snow 6.7

Ice 14.2

10. What impact did speed and the surface have on braking distances? Explain. Stopping distance Go back to your table in Q9. Add two extra columns to the right for each surface. An example is given below. Note: repeat for all surfaces.

Speed (V) Reaction

Distance Dry

asphalt Stopping

Distance 1 Stopping

Distance 2 Gravel Stopping

Distance 1 Stopping

Distance 2 40

50

60

80

100

120


4

Method 1:

A simple method for calculating stopping distance is given below.

Stopping distance = reaction distance + braking distance

11. In the column ‘Stopping Distance 1’, calculate the stopping distances using method 1.

Method 2:

An alternative method for calculating stopping distance is detailed below.

D = 5Vt × (5t + 2.27) 18

where: D = the total stopping distance, in metres

V = the car’s velocity in km/hr t = the driver’s reaction time in seconds

12. Go back to your table. In the ‘Stopping Distance 2’ columns, calculate the stopping

distances using method 2.

13. Was there a difference in your Method 1 & 2 answers? Which is the best method? Explain why / why not. Use method as required in questions 14 - 20.

Complete the following questions using the information you have obtained in this section in relation to stopping distances. Round your answers to one decimal place and show all working. 14. How far will you take to stop when you are travelling at a speed of 80km/hr on a gravel

road?

15. You are driving on a dry asphalt road at 60km/hr.

a) What distance did your car take to stop? b) At the same speed, how much further would it have taken you to stop on a wet asphalt road? c) What should you do if it started raining when you were driving on an asphalt road?

16. When you were driving at 50km/hr on a dry asphalt road, a young child ran onto the road 10 metres in front of you.

a) Would you be able to stop without running over the child? Give a reason for your answer. b) Would the situation have been different if it had been raining? Explain.


5

17. You like to go to the snow.

a) How far will it take you to stop your car at a speed of 60km/hr on snow? b) You drove slowly on the road around the ski lodge because the road was covered with ice. How far will it take you to stop at 15km/hr on the ice?

18. Your family often travels in the country. In dry weather, on an asphalt road, you usually drive at 100km/hr. What is a safe distance for you to leave between your car and the car in front? Explain your answer using your results from above.

19. The maximum speed, in km/hr, a car can be travelling to stop within a distance of D metres can be found by using the formula:

RDV97210

1000+

= where: V = maximum speed in km/hr

D = stopping distance in metres R = road surface index

When you travel on country roads, you like to allow yourself 32 metres to stop.

a) What is the maximum speed you can travel on a gravel road? b) How much faster can you travel on a dry asphalt road than on a gravel road and still maintain a 32m stopping distance?

20. In Victoria a special speed limit of 40 km/hr applies to roads near schools. a) How much shorter is your stopping distance on dry asphalt at 40 km/hr to that at 50

km/hr? b) What is the difference on wet asphalt? c) Using this information, do you think this special speed limit is necessary? Explain.


6

THIS SECTION MUST BE COMPLETED SUMMARY

v Summarise in point form what you discovered in relation to reaction time, stopping and

braking distances.

v What was the most surprising piece of information that you discovered? Explain why.

v What was the hardest calculation/s that you had to obtain?

CONCLUSION

v A recommendation to drivers referring to Sections A, B and C.

v What you have learnt and how you could use this information in the future.

v What transferable skills have you learnt as part of the investigation e.g. ability to use

Excel tables & formulae.

v Explain how this investigation could be improved.

v Would you recommend this investigation to be completed again with a different Senior

VCAL group? Explain why / why not.

v Would you prefer to complete this Investigation altogether or would you have

preferred to complete it separately i.e. breaks / other topics in between? Explain

your answer.


7

EXTENSION – TYRES


8

section c stopping distances · 2018-09-10 · stopping distance = reaction distance + braking...

Documents