91影视

• Mass of spacecraft $\left(m\right)\mathrm{is}900\mathrm{kg}$.
• The force on the spacecraft (F) is 20 N.

Newton鈥檚 second law states that the net force$\stackrel{\mathbf{鈬赌}}{\mathbf{F}}$ on a body with mass mis related to the body鈥檚 acceleration $\stackrel{\mathbf{鈬赌}}{\mathbf{a}}$by,

$\stackrel{\mathbf{鈬赌}}{\mathbf{F}}\mathbf{=}\mathit{m}\stackrel{\mathbf{鈬赌}}{\mathbf{a}}$

Given the mass and force of the spacecraft, we can calculate the acceleration of the spacecraft. In addition, by using the kinematic equation we can determine the distance covered by it in a certain time and find its speed.

Formulae:

$$\begin{gathered} F=ma \\ \left(\mathrm{i}\right) \\ {V}_f=V_0+at \\ \left(\mathrm{ii}\right) \\ s=v_{0}t+\frac{1}{2}a{t}^2 \\ \left(\mathrm{iii}\right) \\ 1\mathrm{day}=86400\mathrm{s} \\ \left(\mathrm{iv}\right) \end{gathered}$$

From equation (i), the acceleration can be written as,

$a=\frac{F}{m}$

Substitute the values in the acceleration equation.

$$\begin{gathered} a=\frac{F}{m} \\ =\frac{20\mathrm{N}}{900\mathrm{kg}} \\ =0.022\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$

Therefore, the acceleration of the spacecraft is $0.022\mathrm{m}/{\mathrm{s}}^2$.

Use the equation (iii) to calculate the distance traveled by the spacecraft in one day. We know the value of acceleration, time and initial velocity.

$$\begin{gathered} s=v_{0}t+\frac{1}{2}a{t}^2 \\ =0+\frac{1}{2}\left(0.022\mathrm{m}/{\mathrm{s}}^2\right)\left(86400s^2\right) \\ =82114560\mathrm{m} \\ =8.21脳{10}^7\mathrm{m} \end{gathered}$$

Therefore, the distance traveled by spacecraft in one day is $8.21脳{10}^7\mathrm{m}$.

Use the equation (ii), acceleration and time value to calculate the speed of the spacecraft in one day,

$$\begin{gathered} v_f=0+at \\ =\left(0.022\mathrm{m}/{\mathrm{s}}^2\right)\left(86400\mathrm{s}\right) \\ =1900.8\mathrm{m}/\mathrm{s} \\ =1.9脳{10}^3 \end{gathered}$$

Therefore, the speed of the spacecraft at the end of one day is $1.9脳{10}^3$.