91影视

The mass of the block is m = 15 kg

The acceleration of the block is$a=2.0m/s^2$

The initial speed of the block is$v_i=10m/s$

The final speed of the block is$v_f=30m/s$

As the system is isolated and moving horizontally, the change in mechanical energy is equal to the change in kinetic energy. Also, by using the formula for average power and instantaneous power the required values can be calculated.

Mechanical energy can be written as

$$\begin{gathered} 鈭�E_{mech}=鈭�K \\ {K}_f=K_i \\ =\frac{1}{2i}m\left(v_f^2-v_i^2\right) \end{gathered}$$

Using the given values intheabove equation, we have,

$$\begin{gathered} 鈭�E_{mech}=\frac{1}{2}脳15kg\left({\left(30m/s\right)}^2-{\left(10m/s\right)}^2\right) \\ =\frac{1}{2}脳15kg\left(800m^2/s^2\right) \\ =6000kg.m^2/s^2\left(\frac{1J}{1kg.m^{2/s^2}}\right) \\ =6000J \end{gathered}$$

Average power is given by

$P_{avg}=\frac{鈭�E}{鈭�t}$

Using the kinetic equation,

$$\begin{gathered} V_f=V_i+at \\ t=\frac{V_f-V_i}{a} \\ t=\frac{30m/s-10m/s}{2m/s^2} \\ t=10s \end{gathered}$$

Using the value of$鈭�E_{mech}$in above equation for average power,

$$\begin{gathered} P_{avg}=\frac{6000J}{10s} \\ =600J/s\left(\frac{1W}{1J/s}\right) \\ =600W \end{gathered}$$

The instantaneous rate of the transfer is expressed as,

$\mathrm{P}=\mathrm{F}\mathrm{惫肠辞蝉胃}$

Since the value of$\cos 胃=1$

For the initial speed of 10 m/s, the instantaneous transfer can be expressed as,

$$\begin{gathered} P=F脳v \\ {P}_{10}=F脳v_i \\ F=ma \\ =15kg脳2m/s^2 \\ =30kg.m/s^2\left(\frac{1N}{1kg.m/s^2}\right) \\ =30N \end{gathered}$$

Using the value of F and initial velocity in equation (2), we get,

$$\begin{gathered} P_{10}=30N脳10m/s \\ =300N.m/s\left(\frac{1W}{1N.m/s}\right) \\ =300W \end{gathered}$$

For the final speed of 30 m/s, the instantaneous transfer is,

${\mathrm{P}}_{30}=\mathrm{F}脳{\mathrm{v}}_{\mathrm{f}}$

Using the value of F and final velocity, we get,

role="math" localid="1661405296794" $$\begin{gathered} P_{30}=30N脳30m/s \\ =900N.m./s\left(\frac{1w}{1N.m/s}\right) \\ =900W \end{gathered}$$