this a 60 kg bicyclist going 2 m/s increased his work output by 1,800 j. what was his final velocity? m/s
When a 60 kg bicyclist accelerates by increasing his work output by 1,800 J, the change in his velocity can be calculated using the principles of energy and motion. In this scenario, the initial velocity of the cyclist is 2 m/s, and by determining the final velocity after the increase in work output, we can gain insights into the impact of this additional energy on his speed.
Calculating the Final Velocity
To determine the final velocity of the 60 kg bicyclist after increasing his work output by 1,800 J, we can use the formula for calculating kinetic energy:
\[ KE = \frac{1}{2}m(v{2}^{2} v{1}^{2}) \]
Where: \( KE \) = change in kinetic energy (in joules) \( m \) = mass of the object (in kilograms) \( v{1} \) = initial velocity of the object (in m/s) \( v{2} \) = final velocity of the object (in m/s)
Given that the initial kinetic energy is: \[ KE_{1} = \frac{1}{2} \times 60 \times (2)^{2} = 120 J \]
And the additional work output is 1,800 J, the total kinetic energy after the increase in work output is:
\[ KE{2} = KE{1} + 1,800 = 120 J + 1,800 J = 1,920 J \]
By rearranging the kinetic energy formula, we can solve for the final velocity:
\[ v_{2} = \sqrt{\frac{2 \times KE}{m}} \]
Plugging in the values for the total kinetic energy and mass of the bicyclist, we get:
\[ v_{2} = \sqrt{\frac{2 \times 1,920}{60}} = \sqrt{\frac{3,840}{60}} = \sqrt{64} = 8 m/s \]
Therefore, the final velocity of the 60 kg bicyclist after increasing his work output by 1,800 J is 8 m/s.
Conclusion
In conclusion, by applying the principles of energy and motion, we were able to determine that the 60 kg bicyclist, initially moving at 2 m/s, increased his velocity to 8 m/s after increasing his work output by 1,800 J. This calculation showcases the relationship between work, energy, and velocity in the context of a moving object, highlighting the direct impact of additional energy on speed.
