Calculate the impulse necessary to stop a 1500 kg car moving at a speed of `"25ms"^(-1).`

Answer

To calculate the impulse necessary to stop a 1500 kg car moving at a speed of 25 m/s, we can follow these steps:

### Step 1: Understand the concept of impulse
Impulse is defined as the change in momentum of an object. It can be calculated using the formula:
\[ \text{Impulse} = \Delta p = m(v_f - v_i) \]
where:
- \( m \) = mass of the object
- \( v_f \) = final velocity
- \( v_i \) = initial velocity

### Step 2: Identify the values given in the problem
From the problem, we have:
- Mass of the car, \( m = 1500 \, \text{kg} \)
- Initial velocity, \( v_i = 25 \, \text{m/s} \)
- Final velocity, \( v_f = 0 \, \text{m/s} \) (since the car comes to a stop)

### Step 3: Calculate the change in momentum
Using the formula for impulse:
\[ \Delta p = m(v_f - v_i) = 1500 \, \text{kg} \times (0 - 25 \, \text{m/s}) \]
This simplifies to:
\[ \Delta p = 1500 \, \text{kg} \times (-25 \, \text{m/s}) = -37500 \, \text{kg m/s} \]

### Step 4: Calculate the impulse
The impulse required to stop the car is equal to the magnitude of the change in momentum:
\[ \text{Impulse} = 37500 \, \text{N s} \quad (\text{since impulse is a vector, we consider the magnitude}) \]

### Final Answer
The impulse necessary to stop the car is:
\[ \text{Impulse} = 37500 \, \text{N s} \]

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