Question

question 6 (mandatory) (1 point) saved
the equation ( v = left( \frac { 2 e } { m }
ight) ^ { \frac { 1 } { 2 } } ) gives the speed, v metres per second, of a moving object with mass m kilograms and kinetic energy e kilojoules.
determine the kinetic energy of a 25 - kg object moving at 16 m/s.
a) 3200 kj
b) 14.1 kj
c) 40 000 kj
d) 20.5 kj

Explanation:

Step1: Square both sides of the equation

Given \(v = (\frac{2e}{m})^{\frac{1}{2}}\), squaring both sides gives \(v^{2}=\frac{2e}{m}\).

Step2: Solve for \(e\)

Multiply both sides of \(v^{2}=\frac{2e}{m}\) by \(m\) to get \(mv^{2}=2e\). Then \(e=\frac{mv^{2}}{2}\).

Step3: Substitute the values of \(m\) and \(v\)

We know \(m = 25\space kg\) and \(v=16\space m/s\). Substitute these values into the formula \(e=\frac{mv^{2}}{2}\). So \(e=\frac{25\times16^{2}}{2}\).
First, calculate \(16^{2}=256\). Then \(25\times256 = 6400\). And \(\frac{6400}{2}=3200\).

Answer:

A. 3200 kJ