Respuesta :
Part A. We are given that a dart travels from rest to a velocity of 30 m/s with an acceleration of 330 m/s^2 to determine the time we will use the following equation of motion:
[tex]v_f=v_0+at[/tex]Where:
[tex]\begin{gathered} v_f,v_0=\text{ final and initial velocities} \\ a=\text{ acceleration } \\ t=\text{ time} \end{gathered}[/tex]Since the dart is launched from rest this means that the initial velocity is zero, therefore:
[tex]v_f=at[/tex]Now, we divide both sides by "a":
[tex]\frac{v_f}{a}=t[/tex]Now, we plug in the values:
[tex]\frac{30\frac{m}{s}}{330\frac{m}{s^2}}=t[/tex]Solving the operation:
[tex]0.09s=t[/tex]Part B. Now, we are asked to determine the distance. To do that we will use the following equation of motion:
[tex]2ad=v_f^2-v_0^2[/tex]Now, we divide both sides by "2a":
[tex]d=\frac{v_f^2-v_0{}^2}{2a}[/tex]Now, we plug in the values:
[tex]d=\frac{(30\frac{m}{s})^2}{2(330\frac{m}{s^2})}[/tex]Solving the operations we get:
[tex]d=1.36m[/tex]Therefore, the distance is 1.36 meters.
