can you use exact values to get the most accurate value to 3dp

Sure, let's refine the solution by using exact values and rounding the final answer to three decimal places.

### Problem Recap:

- **Initial speed**: 15 m/s for 2 minutes
- **Deceleration phase**: 12 seconds (unknown deceleration)
- **Reversing phase**:
  - Acceleration: \(2 \ \text{m/s}^2\) for 8 seconds
  - Deceleration: \(1 \ \text{m/s}^2\) until the vehicle stops

### Step-by-Step Solution:

#### 1. **Distance Covered Before Point B**:

- Initial speed \(u = 15 \ \text{m/s}\)
- Time \(t = 120 \ \text{seconds}\)

The distance covered during this time:
\[
d_A = u \times t = 15 \times 120 = 1800 \ \text{m}
\]

#### 2. **Deceleration to Reach Point B**:

- Deceleration \(a_1\) = unknown
- Time \(t = 12 \ \text{seconds}\)
- Final velocity at point B \(v = 0 \ \text{m/s}\)

Using the equation:
\[
v = u + at
\]
\[
0 = 15 + a_1 \times 12
\]
\[
a_1 = -\frac{15}{12} = -1.25 \ \text{m/s}^2
\]

The distance covered during deceleration (\(d_B\)):
\[
v^2 = u^2 + 2ad
\]
\[
0 = (15)^2 + 2(-1.25)d_B
\]
\[
d_B = \frac{225}{2.5} = 90 \ \text{m}
\]

Total distance to point B:
\[
d_{total} = d_A + d_B = 1800 + 90 = 1890 \ \text{m}
\]

#### 3. **Motion from B to C**:

- **Acceleration phase**:
  - Initial velocity \(u = 0\)
  - Acceleration \(a_2 = 2 \ \text{m/s}^2\)
  - Time \(t = 8 \ \text{seconds}\)

Using:
\[
v_B = u + at = 0 + (2 \times 8) = 16 \ \text{m/s}
\]
Distance covered during acceleration (\(d_C\)):
\[
d_C = ut + \frac{1}{2}at^2 = 0 + \frac{1}{2} \times 2 \times (8)^2 = 64 \ \text{m}
\]

- **Deceleration phase**:
  - Initial velocity \(v_B = 16 \ \text{m/s}\)
  - Final velocity \(v = 0\)
  - Deceleration \(a_3 = -1 \ \text{m/s}^2\)

Using:
\[
v^2 = u^2 + 2ad
\]
\[
0 = (16)^2 + 2(-1)d_{CD}
\]
\[
d_{CD} = \frac{256}{2} = 128 \ \text{m}
\]

Total distance from B to C:
\[
d_{BC} = d_C + d_{CD} = 64 + 128 = 192 \ \text{m}
\]

#### 4. **Total Time for Reversing Motion**:

- Time during acceleration = 8 seconds
- Time during deceleration:

Using:
\[
v = u + at
\]
\[
0 = 16 + (-1)t
\]
\[
t = 16 \ \text{seconds}
\]

Total time to reverse from B to C:
\[
\text{Total time} = 8 + 16 = 24.000 \ \text{seconds}
\]

### Final Answer:
The time it takes for the vehicle to reverse from point B to point C is **24.000 seconds** (to three decimal places).

---

Would you like to go over any particular part of the solution in more detail?

Here are some related questions:
1. How do you use significant figures in calculations?
2. What is the importance of precision in kinematic problems?
3. Can you explain how to calculate the stopping distance of a vehicle?
4. How does initial velocity affect the time and distance of motion?
5. What is the role of deceleration in motion analysis?
6. How do you determine the final velocity in motion problems?
7. What units are used in kinematic equations?
8. How does acceleration relate to the force applied to an object?

**Tip:** When solving physics problems, keep track of units and maintain significant figures to ensure accuracy in your final answer.

Learn how to calculate the time it takes for a vehicle to reverse from point B to point C using kinematic equations. This problem involves initial speed, deceleration, acceleration, and time calculations in physics. Suitable for high school students studying kinematics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation