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Statement-1: When velocity of a particle...

Statement-1: When velocity of a particle is zero then acceleration of particle must be zero at that instant
Statement-2: Acceleration is equal to`a= v ((dv)/(dx)) ` , where v is the velocity at that instant .

A

Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1

B

Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is true, Statement-2 is false

D

Statement-1 is false, Statement-2 is true

Text Solution

AI Generated Solution

The correct Answer is:
To analyze the statements provided in the question, we will evaluate each statement step by step. ### Step 1: Evaluate Statement 1 **Statement 1:** When the velocity of a particle is zero, then the acceleration of the particle must be zero at that instant. **Analysis:** - This statement is **false**. - To understand why, consider a projectile thrown vertically upward. At the highest point of its trajectory, the velocity of the projectile is indeed zero. However, the acceleration due to gravity is still acting on it, which is approximately -9.81 m/s² (downward). - Therefore, it is possible for a particle to have zero velocity while still experiencing non-zero acceleration. ### Step 2: Evaluate Statement 2 **Statement 2:** Acceleration is equal to \( a = v \left( \frac{dv}{dx} \right) \), where \( v \) is the velocity at that instant. **Analysis:** - This statement is **true**. - The relationship can be derived from the definitions of acceleration and velocity. - Acceleration \( a \) is defined as the rate of change of velocity with respect to time, \( a = \frac{dv}{dt} \). - Velocity \( v \) is defined as the rate of change of position with respect to time, \( v = \frac{dx}{dt} \). - By using the chain rule, we can express acceleration in terms of velocity and position: \[ a = \frac{dv}{dt} = \frac{dv}{dx} \cdot \frac{dx}{dt} = v \left( \frac{dv}{dx} \right) \] - Hence, Statement 2 is correct. ### Conclusion - **Statement 1 is false.** - **Statement 2 is true.** Thus, the correct conclusion is that Statement 1 is false and Statement 2 is true. ### Final Answer The correct option is that Statement 1 is false and Statement 2 is true. ---
To analyze the statements provided in the question, we will evaluate each statement step by step. ### Step 1: Evaluate Statement 1 **Statement 1:** When the velocity of a particle is zero, then the acceleration of the particle must be zero at that instant. **Analysis:** - This statement is **false**. - To understand why, consider a projectile thrown vertically upward. At the highest point of its trajectory, the velocity of the projectile is indeed zero. However, the acceleration due to gravity is still acting on it, which is approximately -9.81 m/s² (downward). ...
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