Answer:
(a) [tex]v=\sqrt{\frac{2E}{m}}[/tex]
(b) It is moving at 14 m/s.
Explanation:
(a)
Given:
The energy, [tex]E[/tex], of an object moving with a velocity [tex]v[/tex] is given as:
[tex]E=\frac{1}{2}mv^{2}[/tex], where, [tex]m[/tex] is its mass.
Multiplying both sides by 2, we get
[tex]2E=2\times \frac{1}{2}mv^{2}\\2E=mv^{2}[/tex]
Now, divide both sides by [tex]m[/tex]
[tex]\frac{2E}{m}=\frac{mv^{2}}{m}\\\frac{2E}{m}=v^{2}[/tex]
Taking square root both sides, we get
[tex]\sqrt{\frac{2E}{m}}=\sqrt{v^{2}}\\v=\sqrt{\frac{2E}{m}}[/tex]
Therefore, [tex]v[/tex] in terms of [tex]E[/tex] and [tex]m[/tex] is given as:
[tex]v=\sqrt{\frac{2E}{m}}[/tex]
(b)
Using the above formula, [tex]v=\sqrt{\frac{2E}{m}}[/tex]
Plug in 4900 joules for [tex]E[/tex] and 50 kg for [tex]m[/tex]. Solve for [tex]v[/tex]. This gives,
[tex]v=\sqrt{\frac{2(4900)}{50}}=14\textrm{ m/s}[/tex]
Therefore, it is moving with a speed of 14 m/s.
