The displacement of a particle is related to time by the expression `s=kt^(3)`, what is the dimension of the constant k?

Explanation

To find the dimension of the constant \( k \) in the equation \( s = kt^3 \), we will follow these steps:

### Step 1: Identify the dimensions of displacement \( s \)
Displacement \( s \) is a measure of length. Therefore, the dimension of displacement is:
\[ [s] = L \]
where \( L \) represents length.

### Step 2: Identify the dimensions of time \( t \)
Time \( t \) has the dimension:
\[ [t] = T \]
where \( T \) represents time.

### Step 3: Write the expression for \( s \) in terms of \( k \) and \( t \)
The given equation is:
\[ s = kt^3 \]
We can express the dimensions of the right-hand side:
\[ [s] = [k][t^3] \]

### Step 4: Determine the dimensions of \( t^3 \)
Since the dimension of time \( t \) is \( T \), the dimension of \( t^3 \) is:
\[ [t^3] = T^3 \]

### Step 5: Set up the equation for dimensions
Now we can substitute the dimensions into the equation:
\[ L = [k] \cdot T^3 \]

### Step 6: Solve for the dimension of \( k \)
To isolate \( [k] \), we rearrange the equation:
\[ [k] = \frac{L}{T^3} \]

### Step 7: Express the dimension of \( k \)
Thus, the dimension of the constant \( k \) can be expressed as:
\[ [k] = L T^{-3} \]

### Final Answer
The dimension of the constant \( k \) is \( L T^{-3} \).

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