the stopping distance d of a car after the brakes are applied varies directly as the square of the speed r if a car travelling 80mph can stop in 360ft, how many feet will it take the same car to stop when it is travelling 70mph
d ∝v^2
d = k v^2
for the given...
360 = k(80)^2
k = 360/6400
= 9/160
so if v = 70
d = (9/160)(4900) = 275.625 ft
To solve this problem, we can set up a proportion equation using the given information.
We are told that the stopping distance (d) varies directly as the square of the speed (r). This can be represented as:
d ∝ r^2
Given that a car travelling 80 mph can stop in 360 ft, we can plug these values into the equation:
360 ft ∝ (80 mph)^2
To find the constant of proportionality, we can divide both sides of the equation by (80 mph)^2:
360 ft / (80 mph)^2 = k
Simplifying the equation gives us:
360 ft / 6400 mph^2 = k
Now, we can use the constant of proportionality (k) to find the stopping distance when the car is travelling at 70 mph:
d = k * (70 mph)^2
Plugging in the value of k, we get:
d = (360 ft / 6400 mph^2) * (70 mph)^2
Simplifying the equation gives us:
d = (360 ft / 6400) * 4900
Now, we can calculate the value of d:
d = 360 ft * 4900 / 6400
Simplifying the equation gives us:
d = 27,900 ft / 6400
Finally, we can compute the stopping distance:
d = 4.35 ft
Therefore, when the car is traveling at 70 mph, it will take approximately 4.35 ft to stop.