A body starts to slide over a horizontal surface with an initial velocity of `0.5 kmh^(-1)`.due to friction, it velocity decreases at a rate of `0.05 ms^(-2)` .how much time will it take for body to stop ?\

Answer

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

### Step 1: Convert the initial velocity from km/h to m/s
The initial velocity \( u \) is given as \( 0.5 \, \text{km/h} \). We need to convert this to meters per second (m/s).

\[ u = 0.5 \, \text{km/h} = \frac{0.5 \times 1000 \, \text{m}}{3600 \, \text{s}} = \frac{500}{3600} \, \text{m/s} \approx 0.13889 \, \text{m/s} \]

### Step 2: Identify the acceleration due to friction
The acceleration \( a \) due to friction is given as \( -0.05 \, \text{m/s}^2 \). The negative sign indicates that it is acting in the opposite direction to the motion.

### Step 3: Use the equation of motion
We will use the equation of motion that relates initial velocity, final velocity, acceleration, and time:

\[ v = u + at \]

Where:
- \( v \) is the final velocity (0 m/s, since the body comes to a stop),
- \( u \) is the initial velocity (calculated in Step 1),
- \( a \) is the acceleration (which is negative due to friction),
- \( t \) is the time taken to stop.

Substituting the known values into the equation:

\[ 0 = 0.13889 + (-0.05)t \]

### Step 4: Solve for time \( t \)
Rearranging the equation to solve for \( t \):

\[ 0.05t = 0.13889 \]
\[ t = \frac{0.13889}{0.05} = 2.7778 \, \text{s} \]

Rounding to two decimal places, we find:

\[ t \approx 2.78 \, \text{s} \]

### Final Answer
The time taken for the body to stop is approximately **2.78 seconds**.

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