https://file.aiquickdraw.com/mathbot/file/1727741299458uh8pi3ey.jpg

Convert the following acceleration to the units given in brackets

We are tasked with converting \( 40 \, \text{m} \, \text{min}^{-2} \) into \( \text{km} \, \text{h}^{-2} \).

### Step-by-step conversion:

1. **Convert meters to kilometers**:  
   Since \( 1 \, \text{km} = 1000 \, \text{m} \), we divide the value in meters by 1000.
   \[
   40 \, \text{m} \, \text{min}^{-2} = \frac{40}{1000} \, \text{km} \, \text{min}^{-2} = 0.04 \, \text{km} \, \text{min}^{-2}
   \]

2. **Convert minutes to hours**:  
   Since \( 1 \, \text{hour} = 60 \, \text{minutes} \), we must convert \( \text{min}^{-2} \) into \( \text{h}^{-2} \).  
   We know \( 1 \, \text{min}^{-2} = \left( \frac{1}{60} \, \text{h}^{-1} \right)^2 = \frac{1}{3600} \, \text{h}^{-2} \).
   
   Now multiply:
   \[
   0.04 \, \text{km} \, \text{min}^{-2} = 0.04 \times 3600 \, \text{km} \, \text{h}^{-2} = 144 \, \text{km} \, \text{h}^{-2}
   \]

### Final answer:
\[
40 \, \text{m} \, \text{min}^{-2} = 144 \, \text{km} \, \text{h}^{-2}
\]

Would you like more details or have any questions?

### Related questions:
1. How do you convert acceleration from \( \text{m/s}^2 \) to \( \text{km/h}^2 \)?
2. What are the steps to convert time units in acceleration?
3. How would the conversion change if the original value were in centimeters instead of meters?
4. What is the physical meaning of \( \text{m} \, \text{min}^{-2} \) as a unit of acceleration?
5. Can acceleration be negative, and what does that signify?

### Tip:
Always check your unit conversions step by step, ensuring that both the length and time units are properly converted.

Convert the following acceleration to the units given in brackets: 40 m min^-2 (km h^-2)

Convert the acceleration 40 m/min^2 to km/h^2 with a step-by-step solution. Learn how to handle unit conversions for distance and time, using key formulas. Suitable for high school 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