Question

according to car and driver, an alfa romeo going 70 mph requires 177 feet to stop. assuming that the stopping distance is proportional to the square of the velocity, find the stopping distance required by an alfa romeo going at 20 mph and at 120 mph. at 20 mph, stopping distance = (include units) at 120 mph, stopping distance = (include units)

Explanation:

Step1: Set up the proportionality equation

Let $d$ be the stopping - distance and $v$ be the velocity. Since $d$ is proportional to $v^{2}$, we have $d = kv^{2}$, where $k$ is the constant of proportionality. We know that when $v = 70$ mph, $d = 177$ feet. Substitute these values into the equation: $177=k\times(70)^{2}$. Then $k=\frac{177}{4900}$.

Step2: Find the stopping - distance at 20 mph

Substitute $v = 20$ mph and $k=\frac{177}{4900}$ into $d = kv^{2}$. So $d=\frac{177}{4900}\times(20)^{2}=\frac{177\times400}{4900}=\frac{70800}{4900}\approx14.45$ feet.

Step3: Find the stopping - distance at 120 mph

Substitute $v = 120$ mph and $k=\frac{177}{4900}$ into $d = kv^{2}$. So $d=\frac{177}{4900}\times(120)^{2}=\frac{177\times14400}{4900}=\frac{2548800}{4900}\approx520.16$ feet.

Answer:

At 20 mph, stopping distance = 14.45 feet
At 120 mph, stopping distance = 520.16 feet