If a motorcyclist skids and stops after covering a distance of 15 m.The stopping force acting on the motorcycle by the road is 100N,then work done by the motorcycle on the road is

Options

A. 1500 J
B. `-1500J`
C. 750 J
D. Zero

Explanation

To find the work done by the motorcycle on the road, we can use the formula for work done, which is given by:

\[ \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) \]

Where:
- Work is the work done,
- Force is the force applied,
- Distance is the distance over which the force is applied,
- \( \theta \) is the angle between the force and the direction of motion.

### Step 1: Identify the values
From the problem:
- The stopping force (which is the force exerted by the road on the motorcycle) is \( F = 100 \, \text{N} \).
- The distance covered while skidding is \( d = 15 \, \text{m} \).
- The angle \( \theta \) between the force and the distance is \( 180^\circ \) (since the force exerted by the road is opposite to the direction of motion).

### Step 2: Calculate the work done
Using the formula for work done:

\[ \text{Work} = F \times d \times \cos(180^\circ) \]

Since \( \cos(180^\circ) = -1 \):

\[ \text{Work} = 100 \, \text{N} \times 15 \, \text{m} \times (-1) \]

\[ \text{Work} = -1500 \, \text{J} \]

### Step 3: Conclusion
The work done by the motorcycle on the road is \(-1500 \, \text{J}\). The negative sign indicates that the work is done against the direction of motion, which is expected as the motorcycle is coming to a stop.