Solve 1/2[4kg(5m/s)^2+4kg(0)^2]

$$1 / 2 [ 4 kg ( 5 m / s ) ^ { 2 } + 4 kg ( 0 ) ^ { 2 } ]$$

Evaluate

$$50\times \left(\frac{m}{s}\right)^{2}gk$$

Solution Steps

To raise \frac{5m}{s} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1}{2}\left(4kg\times \frac{\left(5m\right)^{2}}{s^{2}}+4kg\times 0^{2}\right)$$

Express 4\times \frac{\left(5m\right)^{2}}{s^{2}} as a single fraction.

$$\frac{1}{2}\left(\frac{4\times \left(5m\right)^{2}}{s^{2}}kg+4kg\times 0^{2}\right)$$

Calculate 0 to the power of 2 and get 0.

$$\frac{1}{2}\left(\frac{4\times \left(5m\right)^{2}}{s^{2}}kg+4kg\times 0\right)$$

Multiply 4 and 0 to get 0.

$$\frac{1}{2}\left(\frac{4\times \left(5m\right)^{2}}{s^{2}}kg+0kg\right)$$

Anything times zero gives zero.

$$\frac{1}{2}\left(\frac{4\times \left(5m\right)^{2}}{s^{2}}kg+0\right)$$

Anything plus zero gives itself.

$$\frac{1}{2}\times \frac{4\times \left(5m\right)^{2}}{s^{2}}kg$$

Multiply \frac{1}{2} times \frac{4\times \left(5m\right)^{2}}{s^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times \left(5m\right)^{2}}{2s^{2}}kg$$

Cancel out 2 in both numerator and denominator.

$$\frac{2\times \left(5m\right)^{2}}{s^{2}}kg$$

Express \frac{2\times \left(5m\right)^{2}}{s^{2}}k as a single fraction.

$$\frac{2\times \left(5m\right)^{2}k}{s^{2}}g$$

Express \frac{2\times \left(5m\right)^{2}k}{s^{2}}g as a single fraction.

$$\frac{2\times \left(5m\right)^{2}kg}{s^{2}}$$

Expand \left(5m\right)^{2}.

$$\frac{2\times 5^{2}m^{2}kg}{s^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{2\times 25m^{2}kg}{s^{2}}$$

Multiply 2 and 25 to get 50.

$$\frac{50m^{2}kg}{s^{2}}$$

Expand

$$50\times \left(\frac{m}{s}\right)^{2}gk$$

Solution Steps

To raise \frac{5m}{s} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1}{2}\left(4kg\times \frac{\left(5m\right)^{2}}{s^{2}}+4kg\times 0^{2}\right)$$

Express 4\times \frac{\left(5m\right)^{2}}{s^{2}} as a single fraction.

$$\frac{1}{2}\left(\frac{4\times \left(5m\right)^{2}}{s^{2}}kg+4kg\times 0^{2}\right)$$

Calculate 0 to the power of 2 and get 0.

$$\frac{1}{2}\left(\frac{4\times \left(5m\right)^{2}}{s^{2}}kg+4kg\times 0\right)$$

Multiply 4 and 0 to get 0.

$$\frac{1}{2}\left(\frac{4\times \left(5m\right)^{2}}{s^{2}}kg+0kg\right)$$

Anything times zero gives zero.

$$\frac{1}{2}\left(\frac{4\times \left(5m\right)^{2}}{s^{2}}kg+0\right)$$

Anything plus zero gives itself.

$$\frac{1}{2}\times \frac{4\times \left(5m\right)^{2}}{s^{2}}kg$$

Multiply \frac{1}{2} times \frac{4\times \left(5m\right)^{2}}{s^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times \left(5m\right)^{2}}{2s^{2}}kg$$

Cancel out 2 in both numerator and denominator.

$$\frac{2\times \left(5m\right)^{2}}{s^{2}}kg$$

Express \frac{2\times \left(5m\right)^{2}}{s^{2}}k as a single fraction.

$$\frac{2\times \left(5m\right)^{2}k}{s^{2}}g$$

Express \frac{2\times \left(5m\right)^{2}k}{s^{2}}g as a single fraction.

$$\frac{2\times \left(5m\right)^{2}kg}{s^{2}}$$

Expand \left(5m\right)^{2}.

$$\frac{2\times 5^{2}m^{2}kg}{s^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{2\times 25m^{2}kg}{s^{2}}$$

Multiply 2 and 25 to get 50.

$$\frac{50m^{2}kg}{s^{2}}$$