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A particle covers 10m in first 5s and 10m in next 3s. Assuming constant acceleration. Find initial speed, acceleration and distance covered in next 2s. (7/6m/s,1/3m /s², 8.33m) |
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Answer» CASE 1 :- particle COVERS 10m in 5 sec. let intial velocity is u and accelerate is a. so, use formula, S = ut + 1/2 at² here, S = 10m , t = 5 sec so, 10 = 5u + 25a/2 => 2 = u + 5a/2 => 4 = 2u + 5a -----(1) case 2 :- here, velocity after 5 sec = intial velocity in 2nd case. so, initial velocity, v = u + at = u + 5a now, S' = 10m and t' = 3s so, 10 = (u + 5a)3 + 1/2a(3)² 20 = 6u + 30a +9a 20 = 6u + 39a ------(2) solve equations (1) and (2), 20 - 12 = 39a - 15a = 24a 8 = 24a => a = 1/3 m/s² acceleration , a = 1/3 m/s² now, PUT a = 1/3 in equation (1), 4 = 2u + 5/3 => 4 - 5/3 = 2u => 7/6 = u , hence intial velocity , u = 7/6 m/s distance COVERED in next 2 sec = distance covered in (5 + 3 + 2)sec - distance covered in (5 + 3) sec = distance covered in 10sec - distance covered in 8 sec = [7/6 × 10 + 1/2 × 1/3 × 100] - [7/6 × 8 + 1/2 × 1/3 × 64] = 7/6[10 - 8] + 1/6[100 - 64] = 7/3 + 6 = 2.33 + 6 = 8.33 m |
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