Supersonic jet starting from rest accelerates at a constant rate of 60 km/s2. Solve for the velocity of the jet after it travels 260,000 f.

To solve this problem, we need to find the velocity of a supersonic jet after it has traveled a distance of 260,000 feet, given that it starts from rest and accelerates at a constant rate of 60 km/s².

### Step-by-step solution:

1. **Convert all units to a consistent system:**

   - Acceleration is given as 60 km/s². We need to convert this to feet per second squared (\( \text{ft/s}^2 \)).

   \[
   60 \, \text{km/s}^2 = 60 \times 1000 \, \text{m/s}^2 = 60000 \, \text{m/s}^2
   \]

   Since \(1 \, \text{m} = 3.28084 \, \text{ft}\):

   \[
   60000 \, \text{m/s}^2 \times 3.28084 \, \text{ft/m} = 196850.4 \, \text{ft/s}^2
   \]

   - The distance is given as 260,000 feet.

2. **Use the kinematic equation to find the final velocity:**

   The appropriate kinematic equation when starting from rest (initial velocity \(u = 0\)) is:

   \[
   v^2 = u^2 + 2as
   \]

   Where:
   - \(v\) is the final velocity (what we want to find).
   - \(u = 0\) (initial velocity).
   - \(a = 196850.4 \, \text{ft/s}^2\) (acceleration).
   - \(s = 260,000 \, \text{ft}\) (distance).

   Substituting the values into the equation:

   \[
   v^2 = 0 + 2 \times 196850.4 \times 260000
   \]

   \[
   v^2 = 102362208000
   \]

   Solving for \(v\):

   \[
   v = \sqrt{102362208000}
   \]

   Let's calculate this value.The velocity of the supersonic jet after it has traveled 260,000 feet, given the constant acceleration of 60 km/s², is approximately **319,941 ft/s**.

### Summary:
- **Initial velocity (u):** 0 ft/s
- **Acceleration (a):** 196,850.4 ft/s²
- **Distance traveled (s):** 260,000 ft
- **Final velocity (v):** 319,941 ft/s

Would you like more details or have any other questions? Here are some related questions that might interest you:

1. How do you convert between different units of speed, distance, and acceleration?
2. What are other kinematic equations used for uniformly accelerated motion?
3. How does acceleration affect the distance traveled over time in uniformly accelerated motion?
4. What is the importance of converting units when solving physics problems?
5. How can we calculate time taken to reach a certain speed under constant acceleration?

**Tip:** Always ensure all units are consistent when solving physics problems to avoid errors in calculation!

Supersonic jet starting from rest accelerates at a constant rate of 60 km/s². Solve for the velocity of the jet after it travels 260,000 f.

Learn how to calculate the final velocity of a supersonic jet that accelerates at 60 km/s² after traveling 260,000 feet. This step-by-step guide covers kinematic concepts, unit conversions, and the use of motion equations. Suitable for students in Grades 10-12.

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