If a car traveling at 50 mph requires 170 ft to stop, find the stopping distance for a car traveling at
v2 = 60
mph.
To find the stopping distance for a car traveling at 60 mph, we can use the concept of proportionality.
First, let's set up a proportion:
50 mph / 170 ft = 60 mph / x
Where x is the stopping distance we want to find.
To solve for x, we can cross-multiply and solve for x:
50 mph * x = 60 mph * 170 ft
50x = 10200
Now, let's solve for x by dividing both sides of the equation by 50:
x = 10200 / 50
x = 204 ft
Therefore, the stopping distance for a car traveling at 60 mph is 204 ft.
To find the stopping distance for a car traveling at 60 mph, we can use the concept of proportionality.
We know that the stopping distance is directly proportional to the square of the velocity. This means that if we increase the velocity by a certain factor, the stopping distance will increase by the square of that factor.
Let's set up the proportion:
(Stopping distance 1) / (Stopping distance 2) = (Velocity 1^2) / (Velocity 2^2)
The known values are:
Velocity 1 = 50 mph
Stopping distance 1 = 170 ft
Velocity 2 = 60 mph (v2)
Now we can substitute these values into the proportion and solve for Stopping distance 2:
(170 ft) / (Stopping distance 2) = (50 mph)^2 / (60 mph)^2
To solve this equation, we need to convert the velocities from mph to ft/s. Since 1 mph is equal to 1.47 ft/s, we have:
(170 ft) / (Stopping distance 2) = (50 mph * 1.47 ft/s)^2 / (60 mph * 1.47 ft/s)^2
Simplifying the equation gives us:
(170 ft) / (Stopping distance 2) = (73.5 ft/s)^2 / (88.2 ft/s)^2
Now we can cross multiply and solve for Stopping distance 2:
(170 ft) * (88.2 ft/s)^2 = (73.5 ft/s)^2 * (Stopping distance 2)
Solving for Stopping distance 2 gives us:
Stopping distance 2 = (170 ft) * (88.2 ft/s)^2 / (73.5 ft/s)^2
Calculating this expression gives us the stopping distance for a car traveling at v2 = 60 mph.