Answer:[tex]-501\times 10^{-3} N/s[/tex]
Explanation:
Given
[tex]F\left ( t\right )=m\left ( t\right )a\left ( t\right )[/tex]
at t=7 s
m=49 gm
[tex]\frac{\mathrm{d} m}{\mathrm{d} t}=-1 gm/s[/tex]
[tex]a=11 m/s^2[/tex]
[tex]\frac{\mathrm{d} a}{\mathrm{d} t}=-10 m/s^3[/tex]
Differentiating Force
[tex]\frac{\mathrm{d} F(t)}{\mathrm{d} t}=\frac{\mathrm{d} m}{\mathrm{d} t}a+\frac{\mathrm{d} a}{\mathrm{d} t}m[/tex]
[tex]\frac{\mathrm{d} F(t)}{\mathrm{d} t}=-1\times 11-10\times 49=-11-490=-501\times 10^{-3} N/s[/tex]
Answer:
[tex]\frac{dF}{dt} = -0.501\,\frac{N}{s}[/tex]
Explanation:
The rate of change of the force is:
[tex]\frac{dF}{dt} = \frac{dm}{dt}\cdot a(t) + m(t) \cdot \frac{da}{dt}[/tex]
[tex]\frac{dF}{dt} = (-1\times 10^{-3}\,\frac{kg}{s} )\cdot (11\,\frac{m}{s^{2}}) + (0.049\,kg)\cdot (-10\,\frac{m}{s^{3}} )[/tex]
[tex]\frac{dF}{dt} = -0.501\,\frac{N}{s}[/tex]
