Answer:
[tex] \qquad \quad \large \boxed{\bold{ \: \: Velocity = \green{21.36 \: m/s \: \: }}} \\ [/tex]
Explanation:
[tex] \sf{Given:}[/tex]
- A force of 16N acts on a body of mass 90 kg for 2 minutes.
- The body is initially at rest.
[tex] \sf{To \: Find:}[/tex]
- What is the final velocity?
[tex]\large\underline{\mathcal{\blue{SOLUTION:}}} \\ [/tex]
First, we have to find the acceleration of the body:
[tex] \sf{Given:}[/tex]
- [tex] \bold{Force \: (F) = \underline{16N}} \\ [/tex]
- [tex] \bold{Mass \: (m) = \underline{90 \: kg}} \\ [/tex]
According to the question by using the formula we get,
[tex]\begin{gathered}\implies \: \sf\boxed{\bold{ \: \: \: F =\: ma \: \: \: }}\\\end{gathered} [/tex]
[tex] \sf{where,} \\ [/tex]
- [tex] \bold{F = Force} \\ [/tex]
- [tex] \bold{m = Mass} \\ [/tex]
- [tex] \bold{a = Acceleration} \\ [/tex]
So, by putting those values we get,
[tex]\begin{gathered}\implies \: \sf 16 =\: 90a\\\end{gathered} [/tex]
[tex]\begin{gathered}\implies \: \sf \dfrac{16}{90} =\: a\\\end{gathered} [/tex]
[tex]\begin{gathered}\implies \: \sf 0.18 =\: a\\\end{gathered} [/tex]
[tex]\begin{gathered}\implies \: \sf\bold{a =\: 0.18\: m/s^2}\\\end{gathered} [/tex]
Hence, the acceleration of the body is 0.18 m/s² .
Now, we have to find the final velocity of the body:
[tex] \sf{Given:}[/tex]
- [tex] \bold{Initial \: Velocity \: (u) = \underline{ 0 \: m/s}} \\ [/tex]
- [tex] \bold{Acceleration \: (a) = \underline{0.18 \: m/s^2}} \\ [/tex]
- [tex] \begin{aligned}\bold{Time \: Taken \: (t) = \underline{\bold{ 2 \: minutes}}} \\ \bold{= \underline{\bold{(2 × 60) \: seconds}}} \\ \bold{ = \underline{\bold{120 \: seconds}}} \end{aligned} \\ [/tex]
According to the question by using the formula we get,
[tex]\begin{gathered}\implies \: \sf\boxed{\bold{v =\: u + at}}\\\end{gathered} [/tex]
[tex] \sf{where,}[/tex]
- [tex] \bold{v = Final \: Velocity} \\ [/tex]
- [tex] \bold{u = Initial \: Velocity} \\ [/tex]
- [tex] \bold{a = Acceleration} \\ [/tex]
- [tex] \bold{t = Time \: Taken} \\ [/tex]
So, by putting those values we get,
[tex]\begin{gathered}\implies \: \sf v =\: 0 + (0.18 \times 120)\\\end{gathered} [/tex]
[tex]\begin{gathered}\implies \: \sf v =\: 0 + 21.33\\\end{gathered} [/tex]
[tex]\begin{gathered}\implies \: \sf\bold{\underline{v =\: 21.36\: m/s}}\\\end{gathered} [/tex]
[tex] \large \sf{Thus,} \\ [/tex]
[tex]\\\qquad\color{yellow}{\bigstar}\\ \qquad\color{yellow}{\bigstar}-\:\boxed{\bold{\green{\pmb{ \: Velocity = \green{21.36 \: m/s \: }}}}}\: - \bigstar\\\qquad\color{yellow}{\bigstar} [/tex]