Respuesta :
Given:
• Initial velocity = 19 m/s
,• Acceleration = 4.1 m/s²
Let's find how long it will take before its final velocity is equal to three times its initial velocity.
Apply the motion formula:
[tex]v=u+at[/tex]Where:
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time.
Since we are to find the time it will take the final velocity to equal 3 times the initial velocity, we have:
v = 3u
Substitute 3u for v in the equation.
We have:
[tex]3u=u+at[/tex]Substitute values into the formula and solve for t:
[tex]\begin{gathered} 3(19)=19+4.1t \\ \\ 57=19+4.1t \\ \text{ Subtract 19 from both sides} \\ 57-19=19-19+4.1t \\ \\ 38=4.1t \\ \\ \end{gathered}[/tex]Divide both sides by 4.1:
[tex]\begin{gathered} \frac{38}{4.1}=\frac{4.1t}{4.1} \\ \\ 9.17=t \\ \\ t=9.27\text{ s} \end{gathered}[/tex]Therefore, it will take 9.27 seconds before its final velocity is equal to three times its initial velocity.
ANSWER:
9.27 s
