Answer:
[tex]P = 198.1\,N[/tex]
Explanation:
Let assume that crate moves out on a horizontal ground and experiments a constant acceleration. Equations of equilbrium are created by applying Newton's Laws (assumed that movement goes in the positive direction)
[tex]\Sigma F_{x} = P - \mu_{k}\cdot N = m\cdot a[/tex]
[tex]\Sigma F_{y} = N - m\cdot g = 0[/tex]
The acceleration experimented by the crate is:
[tex]a = \frac{10\,\frac{m}{s} }{5\,s}[/tex]
[tex]a = 2\,\frac{m}{s^{2}}[/tex]
By making some algebraic manipulations over equations of equilibrium, an expression for pulling force P is derived:
[tex]P = \mu_{k}\cdot m \cdot g+m\cdot a[/tex]
[tex]P = m\cdot (\mu_{k}\cdot g+a)[/tex]
[tex]P = (50\,kg)\cdot [(0.2)\cdot (9.81\,\frac{m}{s^{2}} )+2\,\frac{m}{s^{2}} ][/tex]
[tex]P = 198.1\,N[/tex]
