Understanding the Relationship

"Acceleration varies directly as the force" means that the acceleration is proportional to the force. This can be expressed mathematically as:

* a = k * F

Where:

* a = acceleration

* F = force

* k = constant of proportionality

Finding the Constant

1. Use the given information: We know that a = 150 m/s² when F = 240 Newtons. Substitute these values into the equation:

150 = k * 240

2. Solve for k: Divide both sides by 240:

k = 150 / 240 = 0.625

Calculating the Force for a Different Acceleration

1. We want to find the force that causes an acceleration of 100 m/s². We know k = 0.625. Let's call the unknown force F'. Plug these values into the equation:

100 = 0.625 * F'

2. Solve for F': Divide both sides by 0.625:

F' = 100 / 0.625 = 160 Newtons

Answer: A force of 160 Newtons will cause an acceleration of 100 m/s².