Final answer:
The speed of the block after 2.50 s, with a force of 25.0 N applied to its mass of 8.35 kg on a frictionless surface, is calculated using Newton's second law and is found to be 7.485 m/s.
Step-by-step explanation:
The question is asking for the speed of a block after a force is applied in the positive x-direction for a certain amount of time. In this scenario, the mass of the block is 8.35 kg, a force of 25.0 N is applied, and we want to know the velocity after 2.50 s. To find the speed, we can use the second law of motion: F = ma, where F is force, m is mass, and a is acceleration.
First, calculate the acceleration by rearranging the formula to a = F/m. Hence, a = 25.0 N / 8.35 kg, which results in an acceleration of approximately 2.994 N/kg or 2.994 m/s². To find the speed after 2.50 s, we can use the formula v = at, where v is the final velocity, a is acceleration, and t is the time. Substituting the values we have, v = 2.994 m/s² x 2.50 s, yielding a final velocity of 7.485 m/s.