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JEE MainPhysicsMotion in One Dimension

A car travels along a straight road. It covers a certain distance at a constant speed of 20 m/s and the remaining distance at a constant speed of 80 m/s . If the average speed of the car for the entire journey is 40 m/s , the distance covered at 20 m/s is 1 n of the total distance. The value of n is ________.

Correct answer

3

Step-by-step solution

Let the total distance be D and the distance covered at 20 m/s be d . The remaining distance is D - d . The time taken for the first part is t₁ = d 20 and for the second part is t₂ = D - d 80 . The average speed is given by: v_ avg = D t₁ + t₂ = 40 D d 20 + D - d 80 = 40 Dividing the numerator and denominator by D and letting x = d D : 1 x 20 + 1 - x 80 = 40 x 20 + 1 - x 80 = 1 40 Multiplying the entire equation by 80 : 4x + 1 - x = 2 3x = 1 x = 1 3 Thus, the distance covered at 20 m/s is 1 3 of the total distance,

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