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To determine the amount of work required to accelerate the baseball, we need to use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
The equation for work is given by:
Work = Change in Kinetic Energy
The change in kinetic energy can be calculated using the equation:
Change in Kinetic Energy = (1/2) * mass * ((final velocity)^2 - (initial velocity)^2)
Given:
Mass of the baseball (m) = 0.145 kg
Initial velocity (v_i) = 0 m/s (as the baseball starts from rest)
Final velocity (v_f) = 38.7 m/s
Let's substitute these values into the equation:
Change in Kinetic Energy = (1/2) * 0.145 kg * ((38.7 m/s)^2 - (0 m/s)^2)
Simplifying:
Change in Kinetic Energy = (1/2) * 0.145 kg * (1500.69 m^2/s^2)
Change in Kinetic Energy = 109.05182 joules
Therefore, the work required to accelerate the baseball to a speed of 38.7 m/s is approximately 109.05 joules.