A truck and a car are moving with equal velocity. On applying the brakes both will stop after certain distance, then

Options

A. Truck will cover less distance before rest
B. Car will cover less distance before rest
C. Both will cover equal distance
D. None

Answer

To solve the problem, we need to analyze the situation where a truck and a car are moving with equal velocity and both apply brakes to come to a stop. We will determine the distance each vehicle travels before coming to a stop.

### Step-by-Step Solution:

1. **Understand the Problem Statement**:
- A truck and a car are moving with equal initial velocities (let's denote this velocity as \( v \)).
- Both vehicles apply brakes and come to a stop after traveling a certain distance.

2. **Identify Forces Acting on the Vehicles**:
- When brakes are applied, a frictional force acts on both vehicles in the opposite direction of their motion.
- The frictional force can be expressed as \( F_f = \mu \cdot N \), where \( \mu \) is the coefficient of friction and \( N \) is the normal force. For both vehicles, this force will depend on their respective weights.

3. **Determine the Acceleration**:
- The acceleration (or deceleration) experienced by both vehicles due to braking can be calculated using Newton's second law:
\[ F = m \cdot a \]
- For the truck (mass \( M \)) and the car (mass \( m \)), the frictional force is:
- Truck: \( F_f = \mu \cdot M \cdot g \)
- Car: \( F_f = \mu \cdot m \cdot g \)
- The acceleration for both vehicles due to braking will be:
\[ a = -\mu \cdot g \]
- Note that the acceleration is negative because it is a deceleration.

4. **Use Kinematic Equation**:
- We can use the kinematic equation to find the stopping distance \( s \):
\[ v^2 = u^2 + 2as \]
- Here, \( v \) (final velocity) is 0 when the vehicles stop, \( u \) (initial velocity) is the same for both vehicles, and \( a \) is the deceleration.
- Rearranging gives:
\[ 0 = u^2 + 2(-\mu g)s \]
\[ s = \frac{u^2}{2\mu g} \]

5. **Compare Distances**:
- Since both vehicles have the same initial velocity \( u \) and experience the same deceleration \( -\mu g \) (assuming the coefficient of friction is the same for both), the stopping distance \( s \) will be the same for both the truck and the car.
- Therefore, both vehicles will cover the same distance before coming to rest.

6. **Conclusion**:
- The correct answer is that both the truck and the car will cover the same distance before stopping.

### Final Answer:
Both the truck and the car will cover the same distance before coming to rest.