1 answer
(click or scroll down)
Explain Bot To find the displacement of the crate, we can use the equation:
\(v^2 = u^2 + 2as\)
where \(v\) is the final velocity, \(u\) is the initial velocity, \(a\) is the acceleration, and \(s\) is the displacement.
In this case, the crate starts from rest, so the initial velocity is \(u = 0\). The final velocity is given as \(v = 9.6 \, \text{m/s}\).
To find the acceleration, we can use Newton's second law of motion:
\(F = ma\)
where \(F\) is the force applied to the crate, and \(m\) is the mass of the crate.
In this case, the force applied to the crate is \(F = 200.0 \, \text{N}\), and the mass of the crate is \(m = 120.0 \, \text{kg}\).
Rearranging the equation for acceleration, we have:
\(a = \frac{F}{m}\)
Substituting the given values, we have:
\(a = \frac{200.0 \, \text{N}}{120.0 \, \text{kg}}\)
Now, we can substitute the values of \(u\), \(v\), and \(a\) into the first equation to find the displacement \(s\):
\(v^2 = u^2 + 2as\)
\((9.6 \, \text{m/s})^2 = (0)^2 + 2 \times \left(\frac{200.0 \, \text{N}}{120.0 \, \text{kg}}\right) \times s\)
Simplifying the equation:
\(92.16 \, \text{m/s}^2 = \frac{400.0}{120.0} \times s\)
\(92.16 \, \text{m/s}^2 = \frac{10}{3} \times s\)
To find \(s\), we can rearrange the equation:
\(s = \frac{92.16 \, \text{m/s}^2}{\frac{10}{3}}\)
Simplifying the equation:
\(s = \frac{92.16 \, \text{m/s}^2 \cdot 3}{10}\)
\(s = \frac{276.48 \, \text{m/s}^2}{10}\)
Finally, calculating \(s\):
\(s = 27.648 \, \text{m}\)
Therefore, the displacement of the crate at the time it reaches a speed of \(9.6 \, \text{m/s}\) is \(27.648 \, \text{m}\).