A truck and a car moving with the same kinetic energy are brought to rest by the application of brakes which provide equal retarding forces. Which of them will come to rest in a shorter distance?

Options

A. The truck
B. The car
C. Both will travel the same distance before coming to rest
D. Cannot be predicted

Explanation

To solve the problem, we need to analyze the situation using the concepts of kinetic energy, work done, and the equations of motion. Here’s a step-by-step solution:

### Step 1: Understand the given information
We have a truck and a car that are both moving with the same kinetic energy (K). They are brought to rest by applying equal retarding forces (F).

### Step 2: Write the equation for kinetic energy
The kinetic energy (K) of an object is given by the formula:
\[ K = \frac{1}{2} mv^2 \]
where \( m \) is the mass and \( v \) is the velocity of the object.

### Step 3: Apply the work-energy theorem
According to the work-energy theorem, the change in kinetic energy is equal to the work done by the forces acting on the object. When the vehicle comes to rest, the final kinetic energy is zero. Therefore, we can write:
\[ \Delta K = K - 0 = K \]
The work done by the retarding force (F) over a distance (D) is:
\[ \text{Work Done} = -F \cdot D \]
(The negative sign indicates that the force is acting in the opposite direction to the motion.)

### Step 4: Set up the equation
For both the truck and the car, we can set up the equation:
\[ K = -F \cdot D \]
This implies:
\[ D = \frac{K}{F} \]

### Step 5: Analyze the results
Since both the truck and the car have the same kinetic energy (K) and are subjected to the same retarding force (F), we can conclude:
\[ D_{\text{truck}} = \frac{K}{F} \]
\[ D_{\text{car}} = \frac{K}{F} \]

### Step 6: Conclusion
Since both distances (D) are equal, we conclude that both the truck and the car will come to rest in the same distance.

### Final Answer
Both the truck and the car will come to rest in the same distance.

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