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Monica is driving on a motorway at a speed of 105 kilometres per hour and has to brake suddenly. She has a reaction time of 1.3 seconds and a braking distance of 54.3 metres.
Stopping distance can be calculated using the following formula
\(\text{stopping distance = {reaction time distance} + {braking distance}}\)
What is Monica's stopping distance? Give your answer to 1 decimal place. (2 marks)
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\(92.2\ \text{metres (to 1 d.p.)}\)
| \(105\ \text{km/hr}\) | \(=105\ 000\ \text{m/hr}\) |
| \(=\dfrac{105\ 000}{60\times 60}\ \text{m/sec}\) | |
| \(=29.166\dots\ \text{m/sec}\) |
| \(\text{Reaction time distance}\) | \(=1.3\times 29.166\dots\) |
| \(=37.916\dots\ \text{metres}\) |
\(\text{Stopping distance}\)
\(\text{ = {Reaction time distance} + {braking distance}}\)
\(=37.916…+54.3\)
\(=92.216\dots\)
\(=92.2\ \text{metres (to 1 d.p.)}\)
Yuan is driving in a school zone at a speed of 30 kilometres per hour and needs to stop immediately to avoid an accident.
It takes him 1.4 seconds to react and his breaking distance is 6.2 metres.
Stopping distance can be calculated using the following formula
\(\text{stopping distance = {reaction time distance} + {braking distance}}\)
What is Yuan's total stopping distance? Give your answer to 1 decimal place. (2 marks)
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\(17.9\ \text{metres (to 1 d.p.)}\)
| \(30\ \text{km/hr}\) | \(=30\ 000\ \text{m/hr}\) |
| \(=\dfrac{30\ 000}{60\times 60}\ \text{m/sec}\) | |
| \(=8.33\dots\ \text{m/sec}\) |
\(\therefore\ \text{Total stopping distance}\)
\(\text{ = {Reaction time distance} + {braking distance}}\)
\(=1.4\times 8.33…+6.2\)
\(=17.866\dots\)
\(=17.9\ \text{metres (to 1 d.p.)}\)
Drake is driving at 80 km/h. He notices a branch on the road ahead and decides to apply the brakes. His reaction time is 1.2 seconds. His 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 Drake’s stopping distance, to the nearest metre? (3 marks)
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\(91\ \text{m (nearest m)}\)
| \(\text{80 km/hr}\) | \(=80\ 000\ \text{m/hr}\) |
| \(=\dfrac{80\ 000}{60\times 60}\ \text{m/sec}\) | |
| \(=22.22\dots\ \text{m/sec}\) |
\(\text{Total stopping distance}\)
\(\text{ = {reaction time distance} + {braking distance}}\)
\(=1.2\times 22.22\dots + 0.01\times 80^2\)
\(=90.66\dots\)
\(=91\ \text{m (nearest m)}\)