Motion of particle is given by equation
`s=(3t^(3)+7t^(2)+14t+8)m`
The value of acceleration of the particle at t = 1 s is

Options

A. `10m//s^(2)`
B. `32m//s^(2)`
C. `23m//s^(2)`
D. `16m//s^(2)`

Answer

To find the acceleration of the particle at \( t = 1 \, \text{s} \), we will follow these steps:

### Step 1: Write down the displacement equation
The displacement \( s \) of the particle is given by the equation:
\[ s = 3t^3 + 7t^2 + 14t + 8 \]

### Step 2: Differentiate the displacement to find velocity
To find the velocity \( v \), we differentiate the displacement \( s \) with respect to time \( t \):
\[ v = \frac{ds}{dt} = \frac{d}{dt}(3t^3 + 7t^2 + 14t + 8) \]
Using the power rule for differentiation:
\[ v = 9t^2 + 14t + 14 \]

### Step 3: Differentiate the velocity to find acceleration
Next, we differentiate the velocity \( v \) with respect to time \( t \) to find the acceleration \( a \):
\[ a = \frac{dv}{dt} = \frac{d}{dt}(9t^2 + 14t + 14) \]
Again, using the power rule:
\[ a = 18t + 14 \]

### Step 4: Substitute \( t = 1 \, \text{s} \) to find acceleration
Now, we substitute \( t = 1 \) into the acceleration equation:
\[ a = 18(1) + 14 = 18 + 14 = 32 \, \text{m/s}^2 \]

### Final Answer
The value of acceleration of the particle at \( t = 1 \, \text{s} \) is:
\[ \boxed{32 \, \text{m/s}^2} \]

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