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Choose all the equations below that are dimensionally correct. In the equations below, F is force, v is velocity, t is time, m is mass, a is acceleration, and k is spring constant. kr = ma – F Oat? = vt – x %3D = = axt %3D O + at = 22 Ft

Choose all the equations below that are dimensionally correct. In the equations below, F is force, v is velocity, t is time, m is mass, a is acceleration, and k is spring constant. kr = ma – F Oat? = vt – x %3D = = axt %3D O + at = 22 Ft

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**Title: Understanding Dimensional Analysis in Physics** **Instruction:** Choose all the equations below that are dimensionally correct. In the equations below, \( F \) is force, \( v \) is velocity, \( t \) is time, \( m \) is mass, \( a \) is acceleration, and \( k \) is the spring constant. **Equations:** 1. \[ kx = ma - F \] 2. \[ at^2 = vt - x \] 3. \[ \frac{x^2}{t} = axt \] 4. \[ \frac{v^2}{x} + at = \frac{x^2}{v} - Ft \] **Explanation:** - The first equation involves the spring constant \( k \), displacement \( x \), mass \( m \), and force \( F \). - The second equation relates acceleration \( a \), time squared \( t^2 \), velocity \( v \), and displacement \( x \). - The third equation features displacement squared divided by time \(\frac{x^2}{t}\), acceleration \( a \), and displacement \( x \) multiplied by time \( t \). - The fourth equation combines velocity squared over displacement \(\frac{v^2}{x}\), acceleration \( a \), time \( t \), displacement squared over velocity \(\frac{x^2}{v}\), and force times time \( Ft \). **Note:** Verify the dimensional consistency of each equation using the fundamental dimensions: mass \([M]\), length \([L]\), and time \([T]\).
Transcribed Image Text:**Title: Understanding Dimensional Analysis in Physics** **Instruction:** Choose all the equations below that are dimensionally correct. In the equations below, \( F \) is force, \( v \) is velocity, \( t \) is time, \( m \) is mass, \( a \) is acceleration, and \( k \) is the spring constant. **Equations:** 1. \[ kx = ma - F \] 2. \[ at^2 = vt - x \] 3. \[ \frac{x^2}{t} = axt \] 4. \[ \frac{v^2}{x} + at = \frac{x^2}{v} - Ft \] **Explanation:** - The first equation involves the spring constant \( k \), displacement \( x \), mass \( m \), and force \( F \). - The second equation relates acceleration \( a \), time squared \( t^2 \), velocity \( v \), and displacement \( x \). - The third equation features displacement squared divided by time \(\frac{x^2}{t}\), acceleration \( a \), and displacement \( x \) multiplied by time \( t \). - The fourth equation combines velocity squared over displacement \(\frac{v^2}{x}\), acceleration \( a \), time \( t \), displacement squared over velocity \(\frac{x^2}{v}\), and force times time \( Ft \). **Note:** Verify the dimensional consistency of each equation using the fundamental dimensions: mass \([M]\), length \([L]\), and time \([T]\).
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