NEETPhysicsMotion in One Dimension
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): A car starting from rest and moving with uniform acceleration covers 5 times the distance in the 3^ rd second as it does in the 1^ st second. Reason (R): For a body starting from rest with uniform acceleration, the distance covered in the n^ th second is directly proportional to n^2 . In the light
Options
- ABoth (A) and (R) are true and (R) is the correct explanation of (A).
- BBoth (A) and (R) are true but (R) is not the correct explanation of (A).
- C(A) is true but (R) is false.
- D(A) is false but (R) is true.
Correct answer
C. (A) is true but (R) is false.
Step-by-step solution
Assertion (A): For a body starting from rest ( u = 0 ) with uniform acceleration a , the distance covered in the n^ th second is given by S_n = a 2 (2n-1) . For n = 1 , S₁ = a 2 (1) . For n = 3 , S₃ = a 2 (5) = 5 S₁ . Thus, the car covers 5 times the distance in the 3^ rd second as it does in the 1^ st second. The Assertion is true. Reason (R): The distance covered in the n^ th second is proportional to (2n-1) , which represents an arithmetic progression of odd numbers (Galileo's law of odd numbers). It is the tota