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Physics · MOTION IN A STRAIGHT LINE
हिन्दीMatch List-I with List-II for calculus relations in kinematics: List-I List-II A \( \frac{dx}{dt} \) I Displacement in time interval \( [t_1, t_2] \) B \( \frac{dv}{dt} \) II Instantaneous velocity C \( v \frac{dv}{dx} \) III Acceleration in terms of position D \( \int_{t_1}^{t_2} v \, dt \) IV Instantaneous acceleration Choose the correct answer from the options given below:
Match List-I with List-II for calculus relations in kinematics:
| List-I | List-II | ||
|---|---|---|---|
| A | \( \frac{dx}{dt} \) | I | Displacement in time interval \( [t_1, t_2] \) |
| B | \( \frac{dv}{dt} \) | II | Instantaneous velocity |
| C | \( v \frac{dv}{dx} \) | III | Acceleration in terms of position |
| D | \( \int_{t_1}^{t_2} v \, dt \) | IV | Instantaneous acceleration |
Choose the correct answer from the options given below:
Correct answer · Option 2
A-(II), B-(IV), C-(III), D-(I)
Explanation
\( \frac{dx}{dt} \) represents instantaneous velocity (A-II). \( \frac{dv}{dt} \) represents instantaneous acceleration (B-IV). \( v \frac{dv}{dx} \) represents acceleration as a function of position (C-III). \( \int_{t_1}^{t_2} v \, dt \) represents displacement over the time interval (D-I).
