Which formula can be used to find velocity if kinetic energy and mass are known?
[tex]v=\sqrt{\frac{1}{2}(K E)(m)}[/tex]
[tex]v=\sqrt{\frac{2 m}{K E}}[/tex]
[tex]v=\sqrt{K E(m)}[/tex]
[tex]v=\sqrt{\frac{2 K E}{m}}[/tex]
Answer (2)
Recall the kinetic energy formula: K E = 2 1 m v 2 .
Rearrange the formula to isolate v 2 : v 2 = m 2 K E .
Take the square root to solve for v : v = m 2 K E .
The correct formula is: v = m 2 K E .
Explanation
Problem Analysis We are given four options for calculating velocity (v) using kinetic energy (KE) and mass (m). Our goal is to identify the correct formula.
Recalling Kinetic Energy Formula The formula for kinetic energy is given by: K E = 2 1 m v 2 We need to rearrange this formula to solve for velocity, v.
Multiplying by 2 First, multiply both sides of the equation by 2: 2 K E = m v 2
Dividing by m Next, divide both sides of the equation by m: m 2 K E = v 2
Taking the Square Root Finally, take the square root of both sides of the equation to solve for v: v = m 2 K E This matches the fourth option provided.
Final Answer Therefore, the correct formula to find velocity when kinetic energy and mass are known is: v = m 2 K E
Examples
Understanding the relationship between kinetic energy, mass, and velocity is crucial in various real-world scenarios. For instance, in car crash analysis, knowing the kinetic energy of a vehicle and its mass allows investigators to estimate the vehicle's velocity just before the impact. This information is vital for accident reconstruction and determining the factors that contributed to the crash. Similarly, in sports, understanding these relationships helps athletes optimize their performance. For example, a baseball player can adjust the mass and velocity of the bat to maximize the kinetic energy transferred to the ball, resulting in a more powerful hit. This concept applies to many other sports, such as golf, tennis, and hockey, where the transfer of kinetic energy is essential for achieving optimal results.
To find the velocity of an object using its kinetic energy and mass, the correct formula is v = m 2 K E . This matches the fourth option provided in the question. This relationship is essential in understanding motion in physics.
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