The displace ment of a body at any time t after starting is given by `s=10t-(1)/(2)(0.2)t^2`. The velocity of the body is zero after:

Options

A. 50 s
B. 100 s
C. 80 s
D. 40 s

Explanation

To find the time at which the velocity of the body becomes zero, we start with the given displacement equation:

\[ s = 10t - \frac{1}{2}(0.2)t^2 \]

### Step 1: Differentiate the displacement equation to find the velocity.
The velocity \( v \) is defined as the rate of change of displacement with respect to time, which can be expressed mathematically as:

\[ v = \frac{ds}{dt} \]

Now, we differentiate the displacement equation with respect to \( t \):

\[ v = \frac{d}{dt}\left(10t - \frac{1}{2}(0.2)t^2\right) \]

### Step 2: Apply the differentiation.
Using the power rule of differentiation:

1. The derivative of \( 10t \) is \( 10 \).
2. The derivative of \( -\frac{1}{2}(0.2)t^2 \) is \( -\frac{1}{2}(0.2) \cdot 2t = -0.2t \).

Thus, we have:

\[ v = 10 - 0.2t \]

### Step 3: Set the velocity equation to zero to find the time.
To find when the velocity is zero, we set the velocity equation equal to zero:

\[ 10 - 0.2t = 0 \]

### Step 4: Solve for \( t \).
Rearranging the equation gives:

\[ 0.2t = 10 \]

Now, divide both sides by \( 0.2 \):

\[ t = \frac{10}{0.2} = 50 \]

### Conclusion:
The velocity of the body is zero after \( t = 50 \) seconds.