https://file.aiquickdraw.com/mathbot/file/1729181044203rx09gyun.jpg

The equation given in the problem is:

\[
d = v_0 t + \frac{1}{2} a t^2
\]

where:
- \( v_0 \) is the initial velocity,
- \( t \) is the time,
- \( a \) is the acceleration,
- \( d \) is the displacement.

Let's analyze each choice to check which one fits the given conditions:

### First option:
- \( v_0 = 0 \, \text{m/s} \)
- \( t = 5 \, \text{seconds} \)
- \( a = -10 \, \text{m/s}^2 \)

Substitute these into the equation:

\[
d = (0)(5) + \frac{1}{2}(-10)(5^2)
\]
\[
d = 0 - \frac{1}{2}(10)(25) = -125 \, \text{m}
\]

This calculation does **not** match the given \( d = 125 \, \text{m} \), so this option is incorrect.

### Second option:
- \( v_0 = 30 \, \text{m/s} \)
- \( t = 5 \, \text{seconds} \)
- \( a = -10 \, \text{m/s}^2 \)

Substitute these values:

\[
d = (30)(5) + \frac{1}{2}(-10)(5^2)
\]
\[
d = 150 - \frac{1}{2}(10)(25) = 150 - 125 = 25 \, \text{m}
\]

This matches the displacement of \( d = 25 \, \text{m} \), so this option is correct.

### Third option:
- \( v_0 = -30 \, \text{m/s} \)
- \( t = 5 \, \text{seconds} \)
- \( a = -10 \, \text{m/s}^2 \)

Substitute these values:

\[
d = (-30)(5) + \frac{1}{2}(-10)(5^2)
\]
\[
d = -150 - 125 = -275 \, \text{m}
\]

This matches the given displacement of \( d = -275 \, \text{m} \), but since the initial velocity is negative and the displacement is large and negative, this seems more consistent with an object moving downward (but not matching the likely scenario described). 

### Conclusion:
The correct answer is the second option:
- \( v_0 = 30 \, \text{m/s} \)
- \( t = 5 \, \text{seconds} \)
- \( a = -10 \, \text{m/s}^2 \)
- \( d = 25 \, \text{m} \)

---

Would you like further details or have any questions about this? 

Here are 5 related questions to expand your understanding:
1. What happens to the displacement if the acceleration is positive instead of negative?
2. How would the displacement change if the initial velocity \( v_0 \) were doubled?
3. What is the significance of the negative sign in acceleration?
4. How would you determine the final velocity of the bottle after 5 seconds?
5. What other kinematic equations could be used to solve for the displacement?

**Tip:** When acceleration is constant, use the appropriate kinematic equations to avoid confusion between velocity, time, and displacement values.

If you wanted to find the speed of a bottle, thrown at 30 seconds, after a time of 5 seconds what would be v_0, t, a, and then solve for d—the position of the bottle from the release point, or the displacement?

Learn how to calculate displacement using the kinematic equation d = v_0 * t + 0.5 * a * t^2. This problem explores concepts of motion under constant acceleration, with detailed step-by-step analysis. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation