The acceleration of a moving particle whose space time equation is given by `s=3t^2+2t-5`, is

Options

A. 6
B. 5
C. 0
D. 1

Answer

To find the acceleration of the moving particle whose space-time equation is given by \( s = 3t^2 + 2t - 5 \), we will follow these steps:

### Step 1: Differentiate the displacement equation to find velocity
The first step is to find the velocity \( v \) by differentiating the displacement \( s \) with respect to time \( t \).

\[ v = \frac{ds}{dt} = \frac{d}{dt}(3t^2 + 2t - 5) \]

### Step 2: Calculate the derivative
Now, we will calculate the derivative:

\[ v = 6t + 2 \]

### Step 3: Differentiate the velocity equation to find acceleration
Next, we find the acceleration \( a \) by differentiating the velocity \( v \) with respect to time \( t \).

\[ a = \frac{dv}{dt} = \frac{d}{dt}(6t + 2) \]

### Step 4: Calculate the derivative
Now, we will calculate the derivative:

\[ a = 6 \]

### Conclusion
Thus, the acceleration of the moving particle is \( 6 \).

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