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a particle starts moving with initial velocity 5m/s. It is accelerating with a constant acceleration 2m/s at an angle 120 degree with the direction of initial veleocity. Find the time after which its speed would be √3 times that of the initial speed |
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Answer» Answer: 5 Sec Explanation: a particle starts moving with initial velocity 5m/s. It is accelerating with a constant acceleration 2m/s at an angle 120 degree with the direction of initial velocity. FIND the TIME after which its speed would be √3 times that of the initial speed Particle Velocity = 5 m/s Acceleration = 2m/s at an angle of 120 Acceleration in direction of Velocity = 2Cos120 = -2Cos60 = - 1 m/s Acceleration in Direction Perpendicular to Velocity = 2Sin120 = √3 m/s Let say the time T after which its speed would be √3 times that of the initial speed Velocity in Original Direction = 5 - T Velocity Perpendicular to Original Direction = 0 + √3T = √3T Velocity at T = √(5 - T)² + (√3T)² = 5√3 Squaring both sides => 25 + T² -10T + 3T² = 75 => 4T² - 10T - 50 = 0 => 2T² - 5T - 25 = 0 => 2T² - 10T + 5T - 25 = 0 => 2T(T - 5) + 5(T -5) = 0 => (2T + 5)(T - 5) = 0 => T = 5 ( Taking only +ve Value of time) After 5 Sec speed would be √3 times that of the initial speed |
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