calculate the work required to be done to stop a car of 1500 kg moving at a velocity of 60 km//h ?

Explanation

To calculate the work required to stop a car of mass 1500 kg moving at a velocity of 60 km/h, we can follow these steps:

### Step 1: Convert the velocity from km/h to m/s
The given velocity of the car is 60 km/h. We need to convert this to meters per second (m/s) using the conversion factor:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]
So, we calculate:
\[ \text{Velocity (v)} = 60 \text{ km/h} \times \frac{5}{18} = 16.66 \text{ m/s} \]

### Step 2: Identify the mass of the car
The mass of the car is given as:
\[ m = 1500 \text{ kg} \]

### Step 3: Determine the final velocity
When the car comes to a stop, its final velocity (vf) is:
\[ vf = 0 \text{ m/s} \]

### Step 4: Use the Work-Energy Theorem
According to the work-energy theorem, the work done (W) is equal to the change in kinetic energy (KE). The formula for kinetic energy is:
\[ KE = \frac{1}{2} mv^2 \]
The initial kinetic energy (KEi) when the car is moving is:
\[ KEi = \frac{1}{2} m v^2 = \frac{1}{2} \times 1500 \text{ kg} \times (16.66 \text{ m/s})^2 \]

### Step 5: Calculate the initial kinetic energy
Calculating the initial kinetic energy:
\[ KEi = \frac{1}{2} \times 1500 \times (16.66)^2 \]
\[ KEi = \frac{1}{2} \times 1500 \times 277.5556 \approx 208167.84 \text{ J} \]

### Step 6: Calculate the work done to stop the car
Since the final kinetic energy (KEf) is 0 (the car is stopped), the work done (W) is equal to the initial kinetic energy:
\[ W = KEf - KEi = 0 - 208167.84 \text{ J} = -208167.84 \text{ J} \]
The negative sign indicates that work is done against the motion of the car.

### Step 7: Convert the work done to kilojoules
To express the work done in kilojoules:
\[ W = -208167.84 \text{ J} = -208.17 \text{ kJ} \]

### Final Answer
The work required to stop the car is approximately:
\[ \boxed{208.17 \text{ kJ}} \]