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Physics · MOTION IN A STRAIGHT LINE
हिन्दीMatch List-I with List-II for kinematic integration formulas: List-I List-II A \( \int_{v_0}^v dv = \int_0^t a \, dt \) I \( v^2 - v_0^2 = 2 a (x - x_0) \) B \( \int_{x_0}^x dx = \int_0^t (v_0 + a t) \, dt \) II Average velocity for constant acceleration C \( \int_{v_0}^v v \, dv = \int_{x_0}^x a \, dx \) III \( v = v_0 + a t \) D \( \bar{v} = \frac{v + v_0}{2} \) IV \( x - x_0 = v_0 t + \frac{1}{2} a t^2 \) Choose the correct answer from the options given below:
Match List-I with List-II for kinematic integration formulas:
| List-I | List-II | ||
|---|---|---|---|
| A | \( \int_{v_0}^v dv = \int_0^t a \, dt \) | I | \( v^2 - v_0^2 = 2 a (x - x_0) \) |
| B | \( \int_{x_0}^x dx = \int_0^t (v_0 + a t) \, dt \) | II | Average velocity for constant acceleration |
| C | \( \int_{v_0}^v v \, dv = \int_{x_0}^x a \, dx \) | III | \( v = v_0 + a t \) |
| D | \( \bar{v} = \frac{v + v_0}{2} \) | IV | \( x - x_0 = v_0 t + \frac{1}{2} a t^2 \) |
Choose the correct answer from the options given below:
Correct answer · Option 2
A-(III), B-(IV), C-(I), D-(II)
Explanation
Integrating acceleration over time yields velocity equation \( v = v_0 + at \) (A-III). Integrating velocity equation yields position \( x - x_0 = v_0 t + \frac{1}{2}at^2 \) (B-IV). Integrating \( v\,dv = a\,dx \) yields \( v^2 - v_0^2 = 2a(x - x_0) \) (C-I). Arithmetic mean speed gives average velocity for uniform acceleration (D-II).
