An Alfa Romeo going at 70 mph requires 169 feet to stop. Assuming that the stopping distance is proportional to the square of velocity, find the stopping distances required by an Alfa Romeo going at 35 mph and at 140 mph (its top speed).
d = kv^2
169 = k*70^2
k = 169/4900
so, d = 169/4900 v^2
plug in v=35 and 140
kmkm
To find the stopping distance required by an Alfa Romeo going at 35 mph, we can set up a proportion using the given information. Let's call the stopping distance for 35 mph "d1":
(70 mph)^2 : (35 mph)^2 = 169 feet : d1
To solve for d1, we can cross-multiply and then divide:
(70 mph)^2 * d1 = (35 mph)^2 * 169 feet
4900 mph^2 * d1 = 1225 mph^2 * 169 feet
Now we can solve for d1:
d1 = (1225 mph^2 * 169 feet) / 4900 mph^2
d1 = 42,175 / 4900
d1 ≈ 8.607 feet
Therefore, an Alfa Romeo going at 35 mph requires approximately 8.607 feet to stop.
Similarly, to find the stopping distance required by an Alfa Romeo going at 140 mph, let's call the stopping distance "d2":
(70 mph)^2 : (140 mph)^2 = 169 feet : d2
Again, we can solve for d2:
d2 = (70 mph)^2 * 169 feet / (140 mph)^2
d2 = 4900 mph^2 * 169 feet / 19600 mph^2
d2 = 830,300 / 19600
d2 ≈ 42.349 feet
Therefore, an Alfa Romeo going at its top speed of 140 mph requires approximately 42.349 feet to stop.
To find the stopping distances required by an Alfa Romeo going at different velocities, we need to first set up a proportion based on the given information.
We are told that at 70 mph, the Alfa Romeo requires 169 feet to stop. Let's call this stopping distance D1. We can write this information as:
70 mph -------> 169 feet (D1)
Now, we can use the proportional relationship based on the square of velocity to find the stopping distances at 35 mph and 140 mph.
Let's assume the stopping distance at 35 mph is D2 and the stopping distance at 140 mph is D3. We can set up the following proportion:
(D1/D2) = (70^2/35^2) -- (1)
(D1/D3) = (70^2/140^2) -- (2)
Now, let's solve equations (1) and (2) to find the values of D2 and D3.
From equation (1):
(D1/D2) = (70^2/35^2)
D1/D2 = 4
Therefore,
D2 = D1/4
D2 = 169/4
D2 = 42.25 feet
So, the stopping distance required by an Alfa Romeo going at 35 mph is 42.25 feet.
From equation (2):
(D1/D3) = (70^2/140^2)
D1/D3 = 0.25
Therefore,
D3 = D1/0.25
D3 = 169/0.25
D3 = 676 feet
So, the stopping distance required by an Alfa Romeo going at 140 mph is 676 feet.
To summarize:
- The stopping distance required by an Alfa Romeo going at 35 mph is approximately 42.25 feet.
- The stopping distance required by an Alfa Romeo going at 140 mph is approximately 676 feet.