https://file.aiquickdraw.com/mathbot/file/172697471355549oqmwed.jpg

The image provides a mathematical expression of Newton's second law in terms of momentum:

\[
\sum \vec{F} = \frac{\Delta \vec{p}}{\Delta t}
\]

This equation can be rewritten as:

\[
\sum \vec{F} \Delta t = \Delta \vec{p}
\]

This expression states that the net force \( \sum \vec{F} \) applied to an object over a time interval \( \Delta t \) results in a change in momentum \( \Delta \vec{p} \).

Now, let's evaluate the provided statements based on this equation:

**A.** If an object experiences zero net force, its momentum will not change.
- This is **true** because \( \sum \vec{F} = 0 \) implies \( \Delta \vec{p} = 0 \), meaning no change in momentum.

**B.** The longer an object experiences a given net force, the more its momentum will change.
- This is **true** because the equation \( \sum \vec{F} \Delta t = \Delta \vec{p} \) shows that as \( \Delta t \) increases, so does \( \Delta \vec{p} \), assuming \( \sum \vec{F} \) remains constant.

**C.** An object can undergo a change in momentum over zero time.
- This is **false** because if \( \Delta t = 0 \), the equation becomes undefined (or no finite change in momentum can occur instantaneously).

**D.** An object can undergo the same change in momentum over different amounts of time.
- This is **true** because if \( \Delta \vec{p} \) is constant, the net force \( \sum \vec{F} \) can vary such that a larger force over a shorter time or a smaller force over a longer time can produce the same change in momentum.

Thus, the correct answers are **A, B, and D**.

Would you like further details or have any questions?

Here are five related questions to expand on this:
1. How does Newton's second law relate to impulse?
2. What is the significance of the time interval \( \Delta t \) in the change of momentum?
3. How does this equation apply in a collision where forces are variable?
4. How would you calculate the force if you know the momentum change and time duration?
5. Can an object have a change in momentum without changing its speed?

**Tip:** Momentum is a vector quantity, so both magnitude and direction need to be considered when analyzing momentum changes.

Use the equation from Newton's second law to select the true statements.

Explore how Newton's second law explains momentum change through the equation ΣF * Δt = Δp. Learn which statements about force, time, and momentum are true based on this fundamental physics concept. Ideal for high school students studying Grades 9-12.

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