Box mass 3kg rests on a smooth top of table.It is connect to hanging box of mass 4kg by mass less string of pulley.3kg box accelerate from velocity of 0.25m/s in 0.65 seconds. How much power is exert?

To find the power exerted, we first need to calculate the net force acting on the 3kg box.

The net force can be calculated using Newton's second law:
F = ma
where F is the net force, m is the mass of the object, and a is the acceleration.

Given that the mass of the 3kg box is 3kg and the acceleration is 0.25m/s^2, we can calculate the net force:
F = 3kg * 0.25m/s^2
F = 0.75N

Next, we need to calculate the work done on the 3kg box.
Work = force * distance
Since the box is accelerating, we can use the equation:
Work = force * distance = force * (1/2) * a * t^2
where t is the time taken for acceleration.

Given that the time taken for acceleration is 0.65 seconds, we can calculate the work done:
Work = 0.75N * (1/2) * 0.25m/s^2 * (0.65s)^2
Work = 0.075J

Finally, we can calculate the power exerted:
Power = work / time
Power = 0.075J / 0.65s
Power = 0.115W

Therefore, the power exerted on the 3kg box is 0.115W.

According to the problem:

$$m_1 = 3\texttt{ kg}$$

$$m_2 = 4\texttt{ kg}$$

$$u = 0.25\texttt{ m/s}$$

$$t = 0.65\texttt{ s}$$

We know,

$$a = \frac{v-u}{t}$$

$$a = \frac{0 - 0.25}{0.65} = -0.3846 \texttt{ m/s}^2$$

The tension in the string is:

$$T = m_1 g - m_1 a = 3\times 9.81 - 3\times (-0.3846) = 32.964 \texttt{ N}$$

The power exerted is:

$$P = T v = 32.964 \times 0.25 = 8.241 \texttt{ W}$$

Therefore the power exerted is 8.241 W.