An 8 kg block accelerates uniformly from rest to a velocity of `4 m s^(-1)` in 40 second. The instantaneous power at the end of 8 second is `P xx 10^(-2)` watt. Find the value of P.

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the acceleration of the block
The acceleration \( a \) can be calculated using the formula:
\[ a = \frac{v_f - v_i}{t} \]
where:
- \( v_f = 4 \, \text{m/s} \) (final velocity)
- \( v_i = 0 \, \text{m/s} \) (initial velocity)
- \( t = 40 \, \text{s} \) (time)

Substituting the values:
\[ a = \frac{4 - 0}{40} = \frac{4}{40} = 0.1 \, \text{m/s}^2 \]

### Step 2: Calculate the velocity at the end of 8 seconds
Using the formula for final velocity:
\[ v = v_i + a \cdot t \]
where:
- \( t = 8 \, \text{s} \)

Substituting the values:
\[ v = 0 + 0.1 \cdot 8 = 0.8 \, \text{m/s} \]

### Step 3: Calculate the force acting on the block
The force \( F \) can be calculated using Newton's second law:
\[ F = m \cdot a \]
where:
- \( m = 8 \, \text{kg} \) (mass of the block)

Substituting the values:
\[ F = 8 \cdot 0.1 = 0.8 \, \text{N} \]

### Step 4: Calculate the instantaneous power at the end of 8 seconds
The instantaneous power \( P \) can be calculated using the formula:
\[ P = F \cdot v \]

Substituting the values:
\[ P = 0.8 \cdot 0.8 = 0.64 \, \text{W} \]

### Step 5: Convert power to the required format
To express the power in the form \( P \times 10^{-2} \):
\[ 0.64 \, \text{W} = 64 \times 10^{-2} \, \text{W} \]

Thus, the value of \( P \) is:
\[ P = 64 \]

### Final Answer
The value of \( P \) is \( 64 \).

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