Suppose that the displacement x of an object is related to time t according to the expression 
x = Bt2.
 What are the dimensions of B?

The given expression for displacement is:

\[
x = Bt^2
\]

Here, \( x \) represents displacement, \( t \) represents time, and \( B \) is a constant whose dimensions we need to find.

### Step 1: Dimensions of Displacement \(x\)
Displacement has the dimension of **length**, denoted as:

\[
[x] = L
\]

### Step 2: Dimensions of Time \(t\)
Time has the dimension denoted as:

\[
[t] = T
\]

### Step 3: Analyzing the Equation
From the given equation:

\[
x = Bt^2
\]

Substitute the dimensions for \(x\) and \(t\):

\[
L = [B] \times T^2
\]

### Step 4: Solve for the Dimensions of \(B\)
Now, isolate \([B]\):

\[
[B] = \frac{L}{T^2}
\]

Thus, the dimensions of \(B\) are:

\[
[B] = L \cdot T^{-2}
\]

### Conclusion:
The dimensions of \(B\) are \( \text{Length} \cdot \text{Time}^{-2} \), or \( L \cdot T^{-2} \).

Would you like more details or further explanations?

Here are five related questions to expand this topic:
1. What is the significance of dimensional analysis in physics?
2. How do we determine the dimensions of velocity from displacement and time?
3. If \( x = Bt^3 \), what would the dimensions of \( B \) be?
4. Can you give an example where dimensional analysis helps verify the correctness of a physical equation?
5. How do the dimensions of acceleration relate to time and displacement?

**Tip:** Dimensional analysis is a useful tool to check the correctness of equations by ensuring both sides have the same dimensions.

Suppose that the displacement x of an object is related to time t according to the expression x = Bt^2. What are the dimensions of B?

Learn how to determine the dimensions of the constant B in the equation x = Bt^2 using dimensional analysis. This problem explores fundamental physics and mathematical concepts, including displacement, time, and dimensional homogeneity. Ideal for students in Grades 9-12.

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