Chapter 12.7, Problem 3P

To determine

To calculate:

To calculate the stopping distance of a car travelling at 64km/h, if stopping distance of a car 80 km/h is 175m and the distance automobile takes to stop varies directly as the square of its speed.

Answer to Problem 3P

The stopping distance is $d=1450$ .

Explanation of Solution

Given information:

The distance automobile takes to stop varies directly as the square of its speed.

let, Speed = s

Distance = d

And $d\prec s^2$

Let k be constant,

  $d=k\cdot s^2$ ...... $\left(1\right)$

Also given stopping distance of a car 80 km/h is 175m

If stopping distance of a car 80 km/h is 175m .

Put the value of distance d and speed s in equation 1 to get the value of k .

  $\begin{array}{l}175cm=k\cdot {\left(\frac{80km}{h}\right)}^2\\ 175cm=k\cdot {\left(\frac{{}^{}80\times 1000}{60\times 60}\right)}^2\\ 175=k\cdot {\left(22.22\frac{m}{s}\right)}^2\end{array}$

Solve further to get k .

  $\begin{array}{l}175=k\cdot 493.72\\ k=\frac{175}{493.72}\\ k=0.354\end{array}$

Now put the value of s and k in equation 1 to get d.

  $\begin{array}{l}d=k\cdot s^2\\ d=0.354\cdot s^2\\ d=0.354\cdot {\left(64\right)}^2\\ d=1449.98\end{array}$

The value of d to the nearest tenth is $d=1450$ .