Final answer:
The force needed to accelerate the block to a speed of 6.0 m/s is 30 N.
Step-by-step explanation:
According to Newton's second law of motion, the force acting on an object is equal to the product of its mass and acceleration. In the given scenario, a block is initially pushed with a force of 15 newtons and accelerates at a rate of 3.0 m/s². To find the force required to accelerate the same block to a speed of 6.0 m/s, we can use the formula:
Force = Mass × Acceleration
Let's assume the mass of the block is 'm'.
- Initial force: 15 N
- Initial acceleration: 3.0 m/s²
- Final speed: 6.0 m/s
Using the formula, we have:
15 N = m × 3.0 m/s²
Then, using the second scenario:
Force needed = m × 6.0 m/s²
To find the force needed, we can substitute the value of 'm' from the first scenario into the second scenario equation:
Force needed = (15 N / 3.0 m/s²) × 6.0 m/s² = 30 N