Question

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)

Answer 1

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

Answer 2

Answer:

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