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Sophie is driving at 70 km/h. She notices a branch on the road ahead and decides to apply the brakes. Her reaction time is 1.5 seconds. Her braking distance (`D` metres) is given by `D = 0.01v^2`, where `v ` is speed in km/h.
Stopping distance can be calculated using the following formula
`text(stopping distance = {reaction time distance} + {braking distance})`
What is Sophie’s stopping distance, to the nearest metre? (3 marks)
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`78\ text{m (nearest m)}`
| `text(70 km/hr)` | `= 70\ 000\ text(m/hr)` |
| `= (70\ 000)/(60 xx 60)\ text(m/sec)` | |
| `= 19.44…\ text(m/sec)` |
`:.\ text(Total stopping distance)`♦ Mean mark 46%.
`=\ text(reaction time distance + braking distance)`
`= 1.5 xx 19.44… + 0.01 xx 70^2`
`= 78.166…`
`= 78\ text{m (nearest m)}`
Doris is driving in a school zone at a speed of 35 kilometres per hour and needs to stop immediately to avoid an accident.
It takes her 1.25 seconds to react and her breaking distance is 5.3 metres.
Stopping distance can be calculated using the following formula
`text(stopping distance = {reaction time distance} + {braking distance})`
What is Doris' total stopping distance? Give your answer to 1 decimal place. (2 marks)
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`17.5\ text{metres (to 1 d.p.)}`
| `35\ text(km/hr)` | `= 35\ 000\ text(m/hr)` |
| `= (35\ 000)/(60 xx 60)\ text(m/sec)` | |
| `= 9.722…\ text(m/sec)` |
`:.\ text(Total stopping distance)`
`=\ text(Reaction time distance) + text(braking distance)`
`= 1.25 xx 9.722… +5.3`
`= 17.452…`
`= 17.5\ text{metres (to 1 d.p.)}`
Claire is driving on a motorway at a speed of 110 kilometres per hour and has to brake suddenly. She has a reaction time of 2 seconds and a braking distance of 59.2 metres.
Stopping distance can be calculated using the following formula
`text(stopping distance = {reaction time distance} + {braking distance})`
What is Claire's stopping distance. (2 marks)
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`120.3\ text{metres (to 1 d.p.)}`
| `110\ text(km/hr)` | `= 110\ 000\ text(m/hr)` |
| `= (110\ 000)/(60 xx 60)\ text(m/sec)` | |
| `= 30.555…\ text(m/sec)` |
| `text(Reaction time distance)` | `=2 xx 30.555…` |
| `= 61.11…\ text(metres)` |
`:.\ text(Stopping distance)`
`=\ text(Reaction time distance + braking distance)`
`= 61.11… + 59.2`
`= 120.311…`
`= 120.3\ text{metres (to 1 d.p.)}`