Find the averasge force needed to accelerate a car weighing 500 kg form rest to 72 km/h in a distance of 25 m.

Explanation

To find the average force needed to accelerate a car weighing 500 kg from rest to 72 km/h in a distance of 25 m, we can follow these steps:

### Step 1: Convert the final velocity from km/h to m/s
The final velocity (v) is given as 72 km/h. We need to convert this to meters per second (m/s).

\[ v = 72 \, \text{km/h} \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{1 \, \text{h}}{3600 \, \text{s}} = 20 \, \text{m/s} \]

### Step 2: Identify initial velocity
The initial velocity (u) is given as 0 m/s since the car starts from rest.

\[ u = 0 \, \text{m/s} \]

### Step 3: Use the equation of motion to find acceleration
We can use the equation of motion:

\[ v^2 = u^2 + 2as \]

Where:
- \( v \) = final velocity = 20 m/s
- \( u \) = initial velocity = 0 m/s
- \( a \) = acceleration
- \( s \) = distance = 25 m

Substituting the known values into the equation:

\[ (20)^2 = (0)^2 + 2a(25) \]

This simplifies to:

\[ 400 = 50a \]

Now, solving for \( a \):

\[ a = \frac{400}{50} = 8 \, \text{m/s}^2 \]

### Step 4: Calculate the average force using Newton's second law
Now that we have the acceleration, we can calculate the average force (F) using Newton's second law:

\[ F = ma \]

Where:
- \( m \) = mass of the car = 500 kg
- \( a \) = acceleration = 8 m/s²

Substituting the values:

\[ F = 500 \times 8 = 4000 \, \text{N} \]

### Final Answer
The average force needed to accelerate the car is **4000 N**.

---