91影视

The given data can be listed below,

• The mass of the soccer ball is, m = 0.420 kg.
• The initial speed of soccer is, $v_i=2鈥�m/s$.
• The constant force acting on the ball is, $F_c=40鈥�N$.
• The final speed of the ball is, $v_f=6.0鈥�m/s$.

According to the work-energy theorem, a system's change in energy is what constitutes work. A moving object's kinetic energy is altered when it is stopped. Therefore work has been done on it.

The total work done on the ball is given by,

$$\begin{gathered} W_{tot}=K_2-K_1 \\ =\frac{1}{2}m{v}_f^2-\frac{1}{2}m{v}_i^2 \end{gathered}$$ 鈥�(颈)

The work done by the force is given by,

$$\begin{gathered} W_{tot}=\stackrel{鈫�}{f}路\stackrel{鈫�}{s} \\ =fs\cos 蠒 \end{gathered}$$ 鈥�(颈颈)

Compare equation (i) and (ii), the distance travelled by the player is given by,

$$\begin{gathered} fs\cos 蠒=\frac{1}{2}m{v}_2^2-\frac{1}{2}m{v}_1^2 \\ s=\frac{1}{2f}m\left(v_f^2{-}_i^2\right) \end{gathered}$$

Substitute all the values in the above,

$$\begin{gathered} s=\frac{1}{2f}m\left(v_f^2{-}_i^2\right) \\ =\frac{1}{2\left(40N\right)}\left(0.42kg\right)\left[{\left(6m/s\right)}^2-{\left(2m/s\right)}^2\right] \\ =\frac{13.44}{40}m \\ =0.168m \end{gathered}$$

Thus, the distance traveled by the player to increase the velocity is 0.168 m.