An object with a kinetic energy of 2160 J has a mass of 120 kg. What is its velocity?
Understand the Problem
The question is asking to determine the velocity of an object given its kinetic energy and mass. This can be solved using the kinetic energy formula: KE = 0.5 * m * v^2, where KE is kinetic energy, m is mass, and v is velocity.
Answer
The velocity is $6 \, \text{m/s}$.
Answer for screen readers
The velocity of the object is $6 , \text{m/s}$.
Steps to Solve
- Identify the given values
The values provided are:
- Kinetic Energy (KE) = 2160 J
- Mass (m) = 120 kg
- Write the kinetic energy formula
The formula for kinetic energy is given by: $$ KE = 0.5 \times m \times v^2 $$
- Rearrange the formula to solve for velocity (v)
To isolate $v$, rearrange the formula as follows: $$ v^2 = \frac{2 \times KE}{m} $$
- Substitute the known values into the formula
Insert the values of KE and m: $$ v^2 = \frac{2 \times 2160}{120} $$
- Simplify the equation
Calculate the right side: $$ v^2 = \frac{4320}{120} = 36 $$
- Find the square root to determine velocity (v)
Take the square root of both sides: $$ v = \sqrt{36} = 6 $$
The velocity of the object is $6 , \text{m/s}$.
More Information
This problem demonstrates the relationship between kinetic energy, mass, and velocity. The kinetic energy of an object is directly related to its mass and the square of its velocity.
Tips
- A common mistake is forgetting to rearrange the formula correctly. Ensure that you isolate $v^2$ before taking the square root.
- Another mistake can be not squaring the velocity after calculating it, so pay attention to the final calculation step.
AI-generated content may contain errors. Please verify critical information
