STANDARD Physics Motion in One Dimension MCQ Question
A particle moving along a straight line has a velocity v m s⁻¹, when it cleared a distance of x m. These two are connected by the relation v = √(49 + x). When its velocity is 1 m s⁻¹, its acceleration is
2 m s⁻²
7 m s⁻²
1 m s⁻²
0.5 m s⁻²
Correct Answer
Detailed Explanation
Given v = √(49 + x). Squaring both sides, v² = 49 + x. Differentiating with respect to t, 2v (dv/dt) = dx/dt. Since v = dx/dt, we have 2v (dv/dt) = v. Solving for dv/dt gives dv/dt = 0.5 m s⁻², which is the acceleration.
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