Stopping Distance, Distance, Speed and Time

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#18938

Distance, Speed and Time

$$d=st$$

$$s=\frac{d}{t}$$

$$t=\frac{d}{s}$$

Stopping Distance

Stopping Distance = Braking distance + Reaction time distance

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#18939

Sarah is travelling at 75 km/h and suddenly has to stop. Her reaction time is 4.2 seconds. She comes to a stop 116.19 m further down the road. Use the braking distance formula d = kv² to find how much further, to the nearest metre, her stopping distance would be if she was travelling 12 km/h faster.

Stopping distance = braking distance + reaction time distance

Find the reaction time distance

75 km/h change to m/s by multiplying  by 1000 to change km to m and dividing by 60 and then divide by 60 again to change from hours to minutes to seconds

speed in m/s = 75 × 1000 ÷ 60 ÷ 60

= 20.83 m/s

reaction time = 4.2 s
reaction time distance = 20.83 × 4.2

= 87.5m

116.19 = braking distance + 87.5

braking distance = 116.19 -87.5

= 28.69 m

substitute this distance into the formula to find k

28.69 =  k × 75²

$$k=\frac{28.69}{5625}$$

k = 0.0051

∴ d = 0.0051v²

 

12 km/h faster = 75 + 12

= 87

find braking distance

d = 0.0051 × 87²

d = 38.6m

find reaction distance

speed in m/s = 87 × 1000 ÷ 60 ÷ 60

= 24.16 m/s

reaction time distance = 24.16 × 4.2

= 101.5 m

stopping distance = 38.6 + 101.5

= 140.1 m

difference is 140.1 – 116.19

= 23.91 m

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#18942

Raine is driving at a speed of 80 km/h. It takes Raine two seconds to react to a dangerous situation before applying the brakes. The stopping distance (in m) is given by the formula: Stopping distance: $$d=\frac{5Vt}{18}+\frac{V^2}{170}$$. How far will Raine travel in her car after applying the brakes using this formula?

Substitute V = 80 and t = 2
$$d=\frac{5\times80\times2}{18}+\frac{80^2}{170}$$
= 82.0915
= 82 m

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#18944

The stopping distance (d) of a scooter travelling with a speed s metres per second is given by the formula d = ¼(s² + s + 2). What is the stopping distance given a speed of  8 metres per second?

substitute s = 8 into the formula

s = ¼ × (8² + 8 + 2)

s = 18.5 m

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#18946

Maryam is driving 80 km/h when she sees a cyclist fall from his bike. Her reaction time is 1.8 seconds and her braking distance is 35 metres. What is her stopping distance?
80 × 1000 ÷ 60 ÷ 60	Step 1: Change 80 km/h into m/s
= 22.2 m	multiply by 1000 to go from km to m and then divide by 60 to go from hours to minutes and divide by 60 again to get to seconds
reaction distance = 22.2 × 1.8 = 40 m	Step 2: her reaction time is 1.8 seconds, so her reaction distance is 1.8 lots 22.2
40 m + 35 m	Step 3: find her total stopping distance = reaction time + braking distance
= 75 m

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