If the 0.3 kg marble was moving at 6m/s at the bottom of the ramp . how much kinetic energy did the marble have? (KE=1/2mv^2 1.8 J 3J 5.4 J 6J

To calculate the kinetic energy of the marble, we can use the formula:<br /><br />\[ KE = \frac{1}{2}mv^2 \]<br /><br />where:<br />- \( KE \) is the kinetic energy,<br />- \( m \) is the mass of the marble,<br />- \( v \) is the velocity of the marble.<br /><br />Given:<br />- \( m = 0.3 \, \text{kg} \)<br />- \( v = 6 \, \text{m/s} \)<br /><br />Now, plug these values into the formula:<br /><br />\[ KE = \frac{1}{2} \times 0.3 \, \text{kg} \times (6 \, \text{m/s})^2 \]<br /><br />First, calculate \( (6 \, \text{m/s})^2 \):<br /><br />\[ (6 \, \text{m/s})^2 = 36 \, \text{m}^2/\text{s}^2 \]<br /><br />Next, multiply by the mass and the factor of \( \frac{1}{2} \):<br /><br />\[ KE = \frac{1}{2} \times 0.3 \, \text{kg} \times 36 \, \text{m}^2/\text{s}^2 \]<br /><br />\[ KE = 0.15 \, \text{kg} \times 36 \, \text{m}^2/\text{s}^2 \]<br /><br />\[ KE = 5.4 \, \text{J} \]<br /><br />Therefore, the kinetic energy of the marble is \( 5.4 \, \text{J} \).<br /><br />So, the correct answer is:<br /><br />\[ \boxed{5.4 \, \text{J}} \]