correlation and causation quick check
a nonzero net force acts on a moving ball, and the ball comes to a stop. which statement is correct about the relationship between the net force and the ball’s movement? (1 point)
an increase in acceleration causes the net force to be nonzero because causation works in both directions.
the net force causes an increase in acceleration because without the force the ball’s velocity would remain the same.
a decrease in acceleration causes the net force to be nonzero because causation works in both directions.
the net force causes a decrease in acceleration because without the force the ball’s velocity would remain the same.

Question

Accepted Answer

To solve this, we use Newton's second law ($F = ma$, where $F$ is net force, $m$ is mass, $a$ is acceleration) and the concept of inertia (an object in motion stays in motion unless a net force acts on it).

### Step 1: Analyze Newton's Second Law and Causation
Newton's second law tells us that net force **causes** acceleration ($F = ma$; force is the cause, acceleration is the effect). Inertia means a moving object (like the ball) will maintain its velocity (speed and direction) unless a net force acts on it.

### Step 2: Evaluate Each Option
- **Option 1**: Acceleration does not cause net force. Force causes acceleration (from $F = ma$), so causation is one - way (force → acceleration), not both. Eliminate.
- **Option 2**: Wait, the ball comes to a stop, so acceleration should be a *deceleration* (negative acceleration, slowing it down). But let's check the logic: The net force (opposing motion) causes acceleration (deceleration, a type of acceleration) because without the force, the ball would keep moving (inertia). Wait, maybe a wording mix - up, but let's check others.
- **Option 3**: Similar to Option 1, acceleration does not cause net force. Force causes acceleration, so causation is not reversed here. Eliminate.
- **Option 4**: Wait, no—if the net force is opposing motion, it causes *deceleration* (a decrease in velocity, which is an acceleration in the opposite direction of motion). But the logic: “without the force the ball’s velocity would remain the same” (inertia) is correct. The net force here is causing a *decrease* in velocity (deceleration), which is an acceleration (since acceleration is a change in velocity). Wait, maybe the options have a wording nuance. Wait, re - evaluating:

Wait, the ball is moving and comes to a stop, so the net force is opposite to motion, causing deceleration (a type of acceleration that reduces velocity). But let's re - check the options:

Wait, the correct physics: A net force causes acceleration (by $F = ma$). If the ball is slowing down, the acceleration is in the opposite direction of velocity (deceleration). The key is causation: force causes acceleration (change in velocity). Without the force, the ball would keep moving (inertia, Newton’s first law).

Now, let's re - analyze the options:

- **First option**: Wrong, because acceleration is caused by force, not the other way.
- **Second option**: The net force causes an increase in acceleration? Wait, no—if the ball is slowing down, the acceleration is a deceleration (a decrease in velocity, but acceleration is a vector; the magnitude could be increasing or not, but the direction is opposite). Wait, maybe the option has a wording error, but let's check the logic of “without the force the ball’s velocity would remain the same” (correct, inertia). The net force causes acceleration (even if it's deceleration, which is a type of acceleration). Wait, maybe the “increase in acceleration” is a misstatement, but let's check the fourth option: “The net force causes a decrease in acceleration because without the force the ball’s velocity would remain the same.” No—acceleration is caused by force. If there is a net force, there is acceleration (change in velocity). Without force, velocity is constant (acceleration = 0). So the net force causes an acceleration (change in velocity), which in this case is a decrease in velocity (deceleration). But the fourth option says “decrease in acceleration”, which is wrong because without force, acceleration is 0, and with force, acceleration is non - zero (so force causes an increase in acceleration from 0 to non - zero, even if the acceleration is decelerating the ball). Wait, I think I made a mistake earlier. Let's start over.

Newton’s first law: An object in motion remains in motion with constant velocity (same speed, same direction) unless a net force acts on it.

Newton’s second law: $F_{net}=ma$ (net force causes acceleration; acceleration is the rate of change of velocity).

In the problem, a non - zero net force acts, and the ball stops (velocity goes from non - zero to zero, so velocity changes → acceleration occurs).

Now, let's analyze each option:

1. “An increase in acceleration causes the net force to be non - zero because causation works in both directions.”
   - From $F = ma$, $F$ causes $a$, not the other way. Causation is force → acceleration, not reverse. Eliminate.

2. “The net force causes an increase in acceleration because without the force the ball’s velocity would remain the same.”
   - Without the force, acceleration is 0 (velocity constant). With the force, there is acceleration (change in velocity). So the net force causes acceleration (a change in velocity). Even though the ball is slowing down (acceleration is opposite to velocity), the force causes an acceleration (from 0 to non - zero). The “increase in acceleration” might be a bit confusing, but the logic about inertia (without force, velocity remains same) is correct, and force causes acceleration. Let's check the other options.

3. “A decrease in acceleration causes the net force to be non - zero because causation works in both directions.”
   - Same as first option: acceleration does not cause force. Force causes acceleration. Eliminate.

4. “The net force causes a decrease in acceleration because without the force the ball’s velocity would remain the same.”
   - Without the force, acceleration is 0. With the force, acceleration is non - zero (so force causes an *increase* in acceleration from 0 to non - zero, not a decrease). So this is wrong.

So the correct option is the second one: “The net force causes an increase in acceleration because without the force the ball’s velocity would remain the same.”

# Answer:
The net force causes an increase in acceleration because without the force the ball’s velocity would remain the same.

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QUESTION IMAGE

Question

Explanation:

Step 1: Analyze Newton's Second Law and Causation

Step 2: Evaluate Each Option

Answer: