A motorcar of mass `1200kg` is moving along a straight line with a uniform velocity of `90 km//h`. Its velocity is slowed down to `18 km//h` in `4s` by an unbalanced external force. Calculate the acceleration and change in momentum. Also, calculate the magnitude of the force required.

Explanation

To solve the problem, we need to calculate the acceleration, change in momentum, and the magnitude of the force required to slow down the motorcar. Let's break it down step by step.

### Step 1: Convert velocities from km/h to m/s
To calculate acceleration, we need to convert the velocities from kilometers per hour (km/h) to meters per second (m/s).

1. **Initial velocity (u)** = 90 km/h
\[ u = 90 \times \frac{1000 \text{ m}}{3600 \text{ s}} = 25 \text{ m/s} \]

2. **Final velocity (v)** = 18 km/h
\[ v = 18 \times \frac{1000 \text{ m}}{3600 \text{ s}} = 5 \text{ m/s} \]

### Step 2: Calculate acceleration
Acceleration (a) can be calculated using the formula:
\[ a = \frac{v - u}{t} \]
where \( t \) is the time taken for the change in velocity.

Substituting the values:
\[ a = \frac{5 \text{ m/s} - 25 \text{ m/s}}{4 \text{ s}} = \frac{-20 \text{ m/s}}{4 \text{ s}} = -5 \text{ m/s}^2 \]

### Step 3: Calculate change in momentum
Momentum (p) is given by the formula:
\[ p = m \cdot v \]
where \( m \) is the mass and \( v \) is the velocity.

1. **Initial momentum (p_initial)**:
\[ p_{\text{initial}} = m \cdot u = 1200 \text{ kg} \cdot 25 \text{ m/s} = 30000 \text{ kg m/s} \]

2. **Final momentum (p_final)**:
\[ p_{\text{final}} = m \cdot v = 1200 \text{ kg} \cdot 5 \text{ m/s} = 6000 \text{ kg m/s} \]

3. **Change in momentum (Δp)**:
\[ \Delta p = p_{\text{final}} - p_{\text{initial}} = 6000 \text{ kg m/s} - 30000 \text{ kg m/s} = -24000 \text{ kg m/s} \]

### Step 4: Calculate the magnitude of the force required
Using Newton's second law, the force (F) can be calculated using the formula:
\[ F = m \cdot a \]

Substituting the values:
\[ F = 1200 \text{ kg} \cdot (-5 \text{ m/s}^2) = -6000 \text{ N} \]

The magnitude of the force is:
\[ |F| = 6000 \text{ N} \]

### Summary of Results
- Acceleration: \( -5 \text{ m/s}^2 \)
- Change in momentum: \( -24000 \text{ kg m/s} \)
- Magnitude of the force required: \( 6000 \text{ N} \)