A body moves along x-axis such that its displacement varies with time as given, `x=7 + 3t + 5t^2`. The average velocity during 3rd second is

Options

A. `28 ms^(-1)`
B. `42 ms^(-1)`
C. `56 ms^(-1)`
D. `15 ms^(-1)`

Answer

To find the average velocity of the body during the 3rd second, we can follow these steps:

### Step 1: Understand the time interval for the 3rd second
The average velocity during the 3rd second refers to the time interval from \( t = 2 \) seconds to \( t = 3 \) seconds.

### Step 2: Write down the displacement equation
The displacement of the body is given by the equation:
\[ x(t) = 7 + 3t + 5t^2 \]

### Step 3: Calculate displacement at \( t = 2 \) seconds
Substituting \( t = 2 \) into the displacement equation:
\[ x(2) = 7 + 3(2) + 5(2^2) \]
Calculating this:
\[ x(2) = 7 + 6 + 20 = 33 \text{ meters} \]

### Step 4: Calculate displacement at \( t = 3 \) seconds
Substituting \( t = 3 \) into the displacement equation:
\[ x(3) = 7 + 3(3) + 5(3^2) \]
Calculating this:
\[ x(3) = 7 + 9 + 45 = 61 \text{ meters} \]

### Step 5: Calculate the average velocity
The average velocity during the 3rd second is given by the formula:
\[ \text{Average Velocity} = \frac{x(3) - x(2)}{3 - 2} \]
Substituting the values we found:
\[ \text{Average Velocity} = \frac{61 - 33}{1} = \frac{28}{1} = 28 \text{ m/s} \]

### Final Answer
The average velocity during the 3rd second is \( 28 \text{ m/s} \).

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