The minimum stopping distance, after a delay of 1 s, for a particular car is modelled by the formula d = 0.006(s + 1)2, where d represents the stopping distance, in metres, and s represents the initial speed, in kilometres per hour.a. Expand and simplify the formula.b. Compare the results in both versions of the formula for an initial speed of 60 km/h.
Question
The minimum stopping distance, after a delay of 1 s, for a particular car is modelled by the formula d = 0.006(s + 1)2, where d represents the stopping distance, in metres, and s represents the initial speed, in kilometres per hour.a. Expand and simplify the formula.b. Compare the results in both versions of the formula for an initial speed of 60 km/h.
Solution
a. To expand and simplify the formula d = 0.006(s + 1)², we first need to expand the square in the brackets:
(s + 1)² = s² + 2s + 1
Then, we multiply each term by 0.006:
d = 0.006s² + 0.012s + 0.006
So, the expanded and simplified formula is d = 0.006s² + 0.012s + 0.006.
b. Now, let's compare the results in both versions of the formula for an initial speed of 60 km/h.
Using the original formula:
d = 0.006(60 + 1)² d = 0.006(61)² d = 0.006 * 3721 d = 22.326 meters
Using the expanded formula:
d = 0.006(60)² + 0.012(60) + 0.006 d = 0.006 * 3600 + 0.72 + 0.006 d = 21.6 + 0.72 + 0.006 d = 22.326 meters
As you can see, the results are the same in both versions of the formula.
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