Question 384497: The algebraic relation d=0.0056s^2+0.14s models the relation between a vehicle's stopping distance d, in meters, and its speed s, in kilometers per hour. What is the fastest you could drive and still be able to stop within 80m? What is the stopping distance for a car travelling at 120km/h? Estimate the length of an average car. How many cars lengths does the stopping distance in (b) correspond to?
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! The algebraic relation d=0.0056s^2+0.14s models the relation between a vehicle's stopping distance d, in meters, and its speed s, in kilometers per hour. What is the fastest you could drive and still be able to stop within 80m?
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Set d to 80m and solve for s:
d=0.0056s^2+0.14s
80=0.0056s^2+0.14s
0=0.0056s^2+0.14s-80
Solving using the quadratic formula yields:
x = {113.26, -141.26}
throw out the negative answer leaving
x = 113.26 km/hour
.
What is the stopping distance for a car travelling at 120km/h?
set x to 120 and solve for d:
d=0.0056s^2+0.14s
d=0.0056(120)^2+0.14(120)
d = 97.44 m
.
Estimate the length of an average car. How many cars lengths does the stopping distance in (b) correspond to?
Assuming the avg length of a car is 4 meters
then
97.44/4 = 24.36 = 24 car lengths
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