In this problem, we calculate the amount of time to accelerate from $v_text{i} = 17.9~mathrm{m/s}$ to $v_text{f} = 22.4~mathrm{m/s}$ with power of $P = 3.05 times 10^{4}~mathrm{W}$. The mass of the object is $m = 1.30 times 10^{3}~mathrm{kg}$.

In this problem, we calculate the amount of time to accelerate from $v_text{i} = 17.9~mathrm{m/s}$ to $v_text{f} = 22.4~mathrm{m/s}$ with power of $P = 3.05 times 10^{4}~mathrm{W}$. The mass of the object is $m = 1.30 times 10^{3}~mathrm{kg}$.

From the definition of power, the work done is also equal to

$$
begin{aligned}
P &= frac{W}{t} \
implies W &= Pt
end{aligned}
$$

Equating the two expresions of $W$ gives us

$$
begin{aligned}
frac{1}{2}m left( v_text{f}^{2} – v_text{i}^{2} right) &= Pt \
implies t &= frac{1}{2} frac{m}{P} left( v_text{f}^{2} – v_text{i}^{2} right) \
&= frac{1}{2} frac{1.30 times 10^{3}~mathrm{kg}}{3.05 times 10^{4}~mathrm{W}}left[ left( 22.4~mathrm{m/s} right)^{2} – left( 17.9~mathrm{m/s} right)^{2} right] \
&= 3.86484~mathrm{s} \
t &= boxed{ 3.86~mathrm{s} }
end{aligned}
$$

$$
t = 3.86~mathrm{s}
$$

In this problem, a pitcher accelerates a hardball of mass $m = 0.14~mathrm{kg}$ from rest to $v_text{f} = 42.5~mathrm{m/s}$ in time $t = 0.060~mathrm{s}$. We calculate the work done on the ball and the power output of the pitcher.

Part A.

The work done on the ball is the change in kinetic energy. Initially, $v_text{i} = 0$. We have

$$
begin{aligned}
W &= Delta KE \
&= frac{1}{2}m left[ v_text{f}^{2} – v_text{i}^{2} right] \
&= frac{1}{2} left( 0.14~mathrm{kg} right) left[ left( 42.5~mathrm{m/s} right)^{2} – 0 right] \
&= 126.43750~mathrm{J} \
W &= boxed{ 130~mathrm{J} }
end{aligned}
$$

Part B.

The power output is the amount of work done per unit time. We have

$$
begin{aligned}
P &= frac{W}{t} \
&= frac{126.43750~mathrm{J}}{0.060~mathrm{s}} \
&= 2107.29167~mathrm{W} \
P &= boxed{ 2100~mathrm{W} }
end{aligned}
$$

$$
begin{aligned}
W &= 130~mathrm{J} \
P &= 2100~mathrm{W}
end{aligned}
$$