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Assertion : Velocity and acceleration of...

Assertion : Velocity and acceleration of a particle are given as,
`v=hati-hatj and a=-2 hati+2 hatj` This is a two dimensional motion with constant acceleration.
Reason : Velocity and acceleration are two constant vectors.

A

If the both Assertion and Reason are true and the Reason is correct explanation of the Assertion.

B

If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

C

If Assertion is true, but the Reason is false.

D

If Assertion is false but the Reason is true.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we will analyze the assertion and the reason provided, and determine whether they are true or false. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states: "Velocity and acceleration of a particle are given as \( \mathbf{v} = \hat{i} - \hat{j} \) and \( \mathbf{a} = -2\hat{i} + 2\hat{j} \). This is a two-dimensional motion with constant acceleration." - Here, \( \mathbf{v} \) and \( \mathbf{a} \) are vectors in two-dimensional space. 2. **Analyzing the Velocity Vector**: - The velocity vector \( \mathbf{v} = \hat{i} - \hat{j} \) indicates that the particle has components in both the x-direction (\( \hat{i} \)) and the y-direction (\( -\hat{j} \)). - This suggests that the particle is indeed moving in two dimensions. 3. **Analyzing the Acceleration Vector**: - The acceleration vector \( \mathbf{a} = -2\hat{i} + 2\hat{j} \) also has components in both the x-direction and the y-direction. - This indicates that the particle is experiencing acceleration in two dimensions. 4. **Checking for Constant Acceleration**: - The assertion claims that the motion is with constant acceleration. Since both the velocity and acceleration vectors are constant (not changing with time), we can conclude that the acceleration is indeed constant. 5. **Conclusion on the Assertion**: - Since both the velocity and acceleration vectors are present in two dimensions and are constant, the assertion is **true**. 6. **Understanding the Reason**: - The reason states: "Velocity and acceleration are two constant vectors." - This is true because both vectors do not change with time. 7. **Final Evaluation**: - The assertion is true, and the reason is also true. However, the reason does not fully justify the assertion since it does not explicitly state that the motion is two-dimensional. - Therefore, while both statements are true, the assertion is not correctly supported by the reason. ### Final Answer: - The assertion is **true** and the reason is **true**, but the reason does not adequately support the assertion.
To solve the question, we will analyze the assertion and the reason provided, and determine whether they are true or false. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states: "Velocity and acceleration of a particle are given as \( \mathbf{v} = \hat{i} - \hat{j} \) and \( \mathbf{a} = -2\hat{i} + 2\hat{j} \). This is a two-dimensional motion with constant acceleration." - Here, \( \mathbf{v} \) and \( \mathbf{a} \) are vectors in two-dimensional space. ...
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