Given below are two statements:
Statement I :A truck and a car moving with same kintic energy are brought to rest by applying breaks which provide equal reytarding forces. Both come to rest in equal distance.
statement `II` A car moving towards east takes a turm an moves towards north, the speed remains unchanged, The acceleration of the car is zero ,< In the light of given statements, choose the most appropriate answer from the option given below

Options

A. Both statement `I` and statement `II` are incorrect.
B. statement `I` is correct but statement `II` is incorrect .
C. Both statement `I`and statement `II` are correct
D. statement `I` is incorrect but statement `II` is correct

Answer

To solve the problem, we will analyze both statements one by one and determine their validity.

### Step 1: Analyze Statement I
**Statement I**: A truck and a car moving with the same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance.

1. **Understanding Kinetic Energy**: The kinetic energy (KE) of an object is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
where \(m\) is the mass and \(v\) is the velocity of the object.

2. **Applying Brakes**: When both vehicles (truck and car) are brought to rest by applying equal retarding forces, we can use the work-energy principle. The work done by the retarding force is equal to the change in kinetic energy:
\[ W = F \cdot d = KE_{initial} - KE_{final} \]
Since both vehicles come to rest, \(KE_{final} = 0\).

3. **Equating Work Done**: Let \(F\) be the equal retarding force and \(d\) be the distance traveled before coming to rest. Thus:
\[ F \cdot d = KE_{initial} \]
Since both vehicles have the same initial kinetic energy and experience the same force, they will come to rest in the same distance \(d\).

**Conclusion for Statement I**: This statement is **correct**.

### Step 2: Analyze Statement II
**Statement II**: A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero.

1. **Understanding Acceleration**: Acceleration is defined as the rate of change of velocity. If the direction of the velocity changes, even if the speed remains constant, the acceleration is not zero.

2. **Turning Motion**: When the car turns from east to north, its direction of velocity changes. This change in direction implies that there is a centripetal acceleration acting towards the center of the turn.

3. **Conclusion for Statement II**: Since the direction of the car's velocity changes, the acceleration cannot be zero. Therefore, this statement is **incorrect**.

### Final Conclusion
- **Statement I** is correct.
- **Statement II** is incorrect.

Thus, the answer is that Statement I is true and Statement II is false.