A motor cycle and a car are moving on a horizontal road with the same velocity. If they are brought to rest by the application of brakes, which provided equal retarding forces, then

Options

A. motorcycle will stop at shorter distance
B. car will stop at a shorter distance
C. both will stop at the same distance
D. nothing can be predicted

Explanation

To solve the problem of determining which vehicle, a motorcycle or a car, will stop at a shorter distance when both are subjected to equal retarding forces, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Both the motorcycle and the car are moving on a horizontal road with the same initial velocity (let's denote it as \( u \)).
- They are brought to rest by applying equal retarding forces.

2. **Identify the Relevant Physics Concepts:**
- We will use the equations of motion, specifically the third equation of motion:
\[ v^2 = u^2 + 2as \]
where:
- \( v \) = final velocity (0 when the vehicle stops)
- \( u \) = initial velocity
- \( a \) = acceleration (negative for retarding force)
- \( s \) = distance traveled before stopping

3. **Set Up the Equation for the Car:**
- For the car, applying the equation of motion:
\[ 0 = u^2 + 2(-a)s_1 \]
Rearranging gives:
\[ s_1 = \frac{u^2}{2a} \]
- Here, \( s_1 \) is the distance traveled by the car before it comes to rest.

4. **Set Up the Equation for the Motorcycle:**
- Similarly, for the motorcycle:
\[ 0 = u^2 + 2(-a)s_2 \]
Rearranging gives:
\[ s_2 = \frac{u^2}{2a} \]
- Here, \( s_2 \) is the distance traveled by the motorcycle before it comes to rest.

5. **Compare the Distances:**
- From the equations derived, we see that:
\[ s_1 = \frac{u^2}{2a} \quad \text{and} \quad s_2 = \frac{u^2}{2a} \]
- This shows that \( s_1 = s_2 \), meaning both the motorcycle and the car will stop after traveling the same distance.

6. **Conclusion:**
- Since both vehicles are subjected to the same initial velocity and equal retarding forces, they will stop after traveling the same distance.

### Final Answer:
Both the motorcycle and the car will stop at the same distance.

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