87.2k views
2 votes
Assume that the stopping distance of van varies directly with the square of the speed. A Van travelling 40 miles per hour can stop in 80'. If Van travelling 64 miles per hour, What is it stopping distance?

User Zulakis
by
9.0k points

1 Answer

1 vote

We have a proportional relationship between the stopping distance d and the square of the speed v^2. This can be written as:


d=k\cdot v^2

where k is a constant we have to find.

We can calculate k knowing that, if the speed is v = 40 miles per hour, the distance is 80 feet. Then:


\begin{gathered} d=k\cdot v^2\longrightarrow k=(d)/(v^2) \\ k=(d)/(v^2)=(80)/(40^2)=(80)/(1600)=0.05 \end{gathered}

NOTE: This value of k correspond to the relation when d is expressed in feet and v in miles per hour.

Now, we can calculate the stopping distance for v = 64 miles per hour:


\begin{gathered} d=k\cdot v^2 \\ d=0.05\cdot64^2=0.05\cdot4096=204.8\text{ ft} \end{gathered}

Answer: 204.8 feet.

User Jibiel
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories