Answer
The average rate at which energy is transferred to the block is $~~600~W$
Work Step by Step
According to part (a), the increase in mechanical energy is $6000~J$
We can find the time it takes the block to accelerate up to $30~m/s$:
$v_f = v_0+at$
$t = \frac{v_f - v_0}{a}$
$t = \frac{30~m/s - 10~m/s}{2.0~m/s^2}$
$t = 10~s$
We can find the average power:
$P_{ave} = \frac{\Delta E}{t}$
$P_{ave} = \frac{6000~J}{10~s}$
$P_{ave} = 600~W$
The average rate at which energy is transferred to the block is $~~600~W$
