In order to find the time it takes, first let's convert the distance from miles per hour to feet per second: calculate the acceleration using Torricelli's equation
[tex]40\text{ mph}=40\cdot1.467\text{ ft/s}=58.7\text{ ft/s}[/tex]
Then, let's :
[tex]\begin{gathered} V^2=V_0^2+2\cdot a\cdot d\\ \\ 0^2=58.7^2+2\cdot a\cdot50\\ \\ 100a=-3445.7\\ \\ a=-34.46\text{ ft/s^^b2} \end{gathered}[/tex]
Now, we calculate the time with the formula below:
[tex]\begin{gathered} \Delta S=V_0t+\frac{at^2}{2}\\ \\ 50=58.7t-17.23t^2\\ \\ -17.23t^2+58.7t-50=0\\ \\ t=\frac{-58.7\sqrt{58.7^2-4\cdot(-17.23)\cdot(-50)}}{2\cdot(-17.23)}\\ \\ t_1=t_2=1.7 \end{gathered}[/tex]
Therefore the time required is 1.7 seconds.
