Final answer:
An object at rest will take 10 seconds to reach a speed of 98 meters per second when falling freely near the Earth's surface, considering that the acceleration due to gravity is 9.8 m/s².
Step-by-step explanation:
To determine how long it takes an object initially at rest to reach a speed of 98 meters per second when falling freely near the Earth's surface, we use the equation of motion under constant acceleration due to gravity. The equation is v = g × t, where v is the final velocity of the object, g is the acceleration due to gravity (9.8 m/s² on Earth), and t is the time. Substituting the given values, we have 98 m/s = 9.8 m/s² × t. Solving for t, we get t = 98 m/s ÷ 9.8 m/s² = 10 seconds.