Question

The energy, E possessed by an object of a mass m kg traveling at a speed of vm/s 1/2 mv^2joules (a) express v interms of E and m (b) if the energy of a 50 kg mass is 4900 joules, how it is moving?

Answer 1

Answer:

(a) $v=\sqrt{\frac{2E}{m}}$

(b) It is moving at 14 m/s.

Explanation:

(a)

Given:

The energy, $E$, of an object moving with a velocity $v$ is given as:

$E=\frac{1}{2}mv^{2}$, where, $m$ is its mass.

Multiplying both sides by 2, we get

$2E=2\times \frac{1}{2}mv^{2}\\2E=mv^{2}$

Now, divide both sides by $m$

$\frac{2E}{m}=\frac{mv^{2}}{m}\\\frac{2E}{m}=v^{2}$

Taking square root both sides, we get

$\sqrt{\frac{2E}{m}}=\sqrt{v^{2}}\\v=\sqrt{\frac{2E}{m}}$

Therefore, $v$ in terms of $E$ and $m$ is given as:

$v=\sqrt{\frac{2E}{m}}$

(b)

Using the above formula, $v=\sqrt{\frac{2E}{m}}$

Plug in 4900 joules for $E$ and 50 kg for $m$. Solve for $v$. This gives,

$v=\sqrt{\frac{2(4900)}{50}}=14\textrm{ m/s}$

Therefore, it is moving with a speed of 14 m/s.