Answer :
We know that
• The initial speed is zero (it starts from rest).
,• The final speed is 55 mi/h.
,• The time elapsed is 11 seconds.
To find the distance traveled, let's use the following formula.
[tex]v^2_f=v^2_0+2ad[/tex]But first, we have to transform 55 mi/h into m/s. We know that 1 mile is equivalent to 1609.34 meters, and 1 hour is equivalent to 3600 seconds.
[tex]55\cdot\frac{mi}{h}\cdot\frac{1609.34m}{1mi}\cdot\frac{1h}{3600\sec}\approx24.6\cdot\frac{m}{s}[/tex]Then, we find the acceleration because we need it to find the distance traveled.
[tex]\begin{gathered} v_f=v_0+at \\ 24.6\cdot\frac{m}{s}=0+a\cdot11\sec \\ a=\frac{24.6\cdot\frac{m}{s}}{11s} \\ a\approx2.2\cdot\frac{m}{s^2} \end{gathered}[/tex](b) The constant acceleration is 2.2 m/s^2.
Now we are able to find the distance traveled.
[tex]\begin{gathered} v^2_f=v^2_0+2ad\to(24.6\cdot\frac{m}{s})^2=0^2+2(2.2\cdot\frac{m}{s^2})d \\ 605.16\cdot\frac{m^2}{s^2}=4.4\cdot\frac{m}{s^2}\cdot d \\ d=\frac{605.16\cdot\frac{m^2}{s^2}}{4.4\cdot\frac{m}{s^2}} \\ d\approx137.5m \end{gathered}[/tex]