The braking distance of a car, in metres, is directly proportional to the square of its speed in km/h, and can be represented by the equation
braking distance = k × (speed)²
where k is the constant of variation - HSC - SSCE Mathematics Standard - Question 22 - 2023 - Paper 1
Question 22
The braking distance of a car, in metres, is directly proportional to the square of its speed in km/h, and can be represented by the equation
braking distance = k ×... show full transcript
Worked Solution & Example Answer:The braking distance of a car, in metres, is directly proportional to the square of its speed in km/h, and can be represented by the equation
braking distance = k × (speed)²
where k is the constant of variation - HSC - SSCE Mathematics Standard - Question 22 - 2023 - Paper 1
Step 1
Find the value of k.
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Answer
Given the equation for braking distance:
extbrakingdistance=k×(speed)2
We know that the braking distance when the speed is 50 km/h is 20 m:
20=k×(50)2
First, we calculate (50)²:
(50)2=2500
Now substituting this value back into the equation gives:
20=k×2500
To solve for k, we divide both sides by 2500:
k=250020
Calculating this results in:
k=0.008
Step 2
What is the braking distance when the speed of the car is 90 km/h?
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Answer
Using the value of k found in part (a), we can substitute it back into the braking distance formula:
extbrakingdistance=0.008×(speed)2
Substituting the speed of 90 km/h into the equation:
