A body of mass `2kg` starts from rest and moves with uniform acceleration. It acquires a velocity `20ms^-1` in `4s`.
The power exerted on the body at `2s` is

Options

A. (a) `50W`
B. (b) `100W`
C. (c) `150W`
D. (d) `200W`

Explanation

To solve the problem step by step, we will follow the principles of kinematics and the definition of power.

### Step 1: Determine the acceleration of the body

We know that the body starts from rest and acquires a velocity of \(20 \, \text{m/s}\) in \(4 \, \text{s}\). We can use the equation of motion:

\[ v = u + at \]

Where:
- \(v\) = final velocity = \(20 \, \text{m/s}\)
- \(u\) = initial velocity = \(0 \, \text{m/s}\) (starts from rest)
- \(a\) = acceleration (unknown)
- \(t\) = time = \(4 \, \text{s}\)

Substituting the known values into the equation:

\[ 20 = 0 + a \cdot 4 \]

Solving for \(a\):

\[ a = \frac{20}{4} = 5 \, \text{m/s}^2 \]

### Step 2: Calculate the force acting on the body

Using Newton's second law, the force \(F\) can be calculated as:

\[ F = m \cdot a \]

Where:
- \(m\) = mass of the body = \(2 \, \text{kg}\)
- \(a\) = acceleration = \(5 \, \text{m/s}^2\)

Substituting the values:

\[ F = 2 \cdot 5 = 10 \, \text{N} \]

### Step 3: Calculate the velocity at \(t = 2 \, \text{s}\)

We can use the same equation of motion to find the velocity at \(t = 2 \, \text{s}\):

\[ v = u + at \]

Substituting the known values:

\[ v = 0 + 5 \cdot 2 = 10 \, \text{m/s} \]

### Step 4: Calculate the power exerted on the body at \(t = 2 \, \text{s}\)

Power \(P\) is defined as the product of force and velocity:

\[ P = F \cdot v \]

Substituting the values we found:

\[ P = 10 \, \text{N} \cdot 10 \, \text{m/s} = 100 \, \text{W} \]

### Final Answer

The power exerted on the body at \(t = 2 \, \text{s}\) is \(100 \, \text{W}\).

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