A truck and a car are moving with velocity v towards each other. They collide head in and stops after some time. If the time of collision is 1 sec, which vehicle will have maximum change in momentum?

Options

A. Car
B. Truck
C. Both will have same
D. None of the above

Explanation

To solve the problem of which vehicle will have the maximum change in momentum after a collision between a truck and a car, we can follow these steps:

### Step 1: Understand the concept of momentum
Momentum (p) is defined as the product of mass (m) and velocity (v):
\[ p = m \times v \]
In the case of a collision, we need to consider the initial and final momentum of both vehicles.

### Step 2: Define the masses and velocities
Let:
- Mass of the car = \( m_c \)
- Mass of the truck = \( m_t \) (where \( m_t > m_c \))
- Initial velocity of the car = \( v \) (towards the truck)
- Initial velocity of the truck = \( v \) (towards the car)

### Step 3: Calculate initial momentum
The initial momentum of the car (before collision) is:
\[ p_{c_i} = m_c \times v \]
The initial momentum of the truck (before collision) is:
\[ p_{t_i} = m_t \times v \]

### Step 4: Determine final momentum after collision
After the collision, both vehicles come to a stop. Therefore, the final momentum for both the car and the truck is:
\[ p_{c_f} = 0 \]
\[ p_{t_f} = 0 \]

### Step 5: Calculate change in momentum
The change in momentum for the car is:
\[ \Delta p_c = p_{c_f} - p_{c_i} = 0 - (m_c \times v) = -m_c \times v \]
The change in momentum for the truck is:
\[ \Delta p_t = p_{t_f} - p_{t_i} = 0 - (m_t \times v) = -m_t \times v \]

### Step 6: Compare the magnitudes of change in momentum
The magnitudes of the changes in momentum are:
- For the car: \( |\Delta p_c| = m_c \times v \)
- For the truck: \( |\Delta p_t| = m_t \times v \)

Since \( m_t > m_c \), it follows that:
\[ |\Delta p_t| > |\Delta p_c| \]

### Conclusion
Thus, the truck will have a maximum change in momentum compared to the car after the collision.