Question

a particle with certain initial velocity is uniformly accelerated . if it covers 25 m in 5th second and 49m in 7th second of it's motion determine the distance travelled by it in 10sec.​

Answer 1

Answer:

S = v t + 1/2 a t^2

S(5) - S(4) = v (5 - 4) + 1/2 a (25 - 16)      traveled in 5th sec

S(7) - S(6) = v (7 - 6) + 1/2 a (49 - 36)          "       "       7th  "

25 = v + a/2 * 9

49 = v + a/2 * 13

24 = 2 a        subtracting equations

a = 12

2 v = 74 - 6 * 22       adding equations

v = -29

S(10) = -29 * 10 + 12 * 100 / 2 = 310 m      total distance in 10 sec

Check:

S(5) - S(4) = -29 * (5 - 4) + 1/2 * 12 (25 - 16) = 54 - 29 = 25