A vehicle of mass 500 kg is moving with a velocity of `15ms^(-1)`. It is brought to rest by a retarding force. Find the distance moved by the vehicle before coming to rest, if the sliding friction between the tyres and the road is 3000N.

Answer

To find the distance moved by the vehicle before coming to rest, we can follow these steps:

### Step 1: Identify the given values
- Mass of the vehicle (m) = 500 kg
- Initial velocity (u) = 15 m/s
- Retarding force (F) = 3000 N

### Step 2: Calculate the retardation (a)
Using Newton's second law of motion, we can find the acceleration (retardation in this case) using the formula:
\[ a = \frac{F}{m} \]

Substituting the values:
\[ a = \frac{3000 \, \text{N}}{500 \, \text{kg}} \]
\[ a = 6 \, \text{m/s}^2 \]

### Step 3: Use the kinematic equation to find the distance (s)
We can use the kinematic equation that relates initial velocity, final velocity, acceleration, and distance:
\[ v^2 = u^2 + 2as \]
Where:
- Final velocity (v) = 0 m/s (since the vehicle comes to rest)
- Initial velocity (u) = 15 m/s
- Acceleration (a) = -6 m/s² (negative because it is retardation)

Rearranging the equation to solve for distance (s):
\[ 0 = (15)^2 + 2(-6)s \]
\[ 0 = 225 - 12s \]
\[ 12s = 225 \]
\[ s = \frac{225}{12} \]
\[ s = 18.75 \, \text{m} \]

### Final Answer
The distance moved by the vehicle before coming to rest is **18.75 meters**.

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