Question

1. calculate the speed of a 5.2 kg object that possesses 26.1 j of kinetic energy.

Explanation:

The formula for kinetic energy is \( KE = \frac{1}{2}mv^2 \), where \( KE \) is the kinetic energy, \( m \) is the mass, and \( v \) is the velocity (speed). We need to solve for \( v \).

Step 1: Rearrange the kinetic energy formula to solve for \( v \)

Starting with \( KE = \frac{1}{2}mv^2 \), we can multiply both sides by 2 to get \( 2KE = mv^2 \). Then divide both sides by \( m \) to obtain \( v^2 = \frac{2KE}{m} \). Finally, take the square root of both sides: \( v = \sqrt{\frac{2KE}{m}} \).

Step 2: Substitute the given values

We know that \( KE = 26.1 \, \text{J} \) and \( m = 5.2 \, \text{kg} \). Plugging these values into the formula for \( v \):

\( v = \sqrt{\frac{2 \times 26.1}{5.2}} \)

First, calculate the numerator: \( 2 \times 26.1 = 52.2 \)

Then, divide by the mass: \( \frac{52.2}{5.2} \approx 10.0385 \)

Step 3: Take the square root

Now, take the square root of \( 10.0385 \):

\( v \approx \sqrt{10.0385} \approx 3.17 \, \text{m/s} \) (rounded to two decimal places)

Answer:

The speed of the object is approximately \( \boldsymbol{3.17 \, \text{m/s}} \) (or more precisely, if we keep more decimal places during calculation, it can be checked further, but this is a reasonable approximation).